scientific article
From MaRDI portal
zbMath0292.10016MaRDI QIDQ4043127
Dale H. Husemoller, John W. Milnor
Publication date: 1973
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sums of squares and representations by other particular quadratic forms (11E25) Algebraic theory of quadratic forms; Witt groups and rings (11E81) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Lattices and convex bodies (number-theoretic aspects) (11H06) Bilinear and Hermitian forms (11E39) Quadratic and bilinear forms, inner products (15A63)
Related Items
Manifolds which admit maps with finitely many critical points into spheres of small dimensions, On classical upper bounds for slice genera, Local densities and explicit bounds for representability by a quadratic form, Smooth 2-spheres in homology K3 surfaces, Universal gradings of orders, Non-zero degree maps between \(2n\)-manifolds, Congruence of Hermitian matrices over some localizations of \(C[z, z^{- 1}\)], The homology of cyclic branched covers of \(S^ 3\), Computing with quadratic forms over number fields, Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\), About the Witt rings of function fields of algebroid quadratic quasihomogeneous surfaces, On the conservativity of the functor assigning to a motivic spectrum its motive, Conformal characters and theta series, Complex surface singularities from the combinatorial point of view, Minimal vectors in the second exterior power of a lattice, Codes and Siegel modular forms, Adele groups and Siegel-Tamagawa formulas, Equivalence classes of fields of \(2\)-planes and two kinds of almost complex structures on compact four-dimensional manifolds, Elementary geometry on the integer lattice, The Witt group of a discretely valued field, The intersection form of the result of gluing manifolds with degenerate intersection forms, Genus and symmetry in homotopy theory, The regular octagon and the signature of nonsingular integral quadratic forms. With an appendice of Géraldine Gahide., Right-angled Coxeter polytopes, hyperbolic six-manifolds, and a problem of Siegel, \( \mathcal{N}=2 \) supersymmetric gauge theory on connected sums of \(S^{2} \times S^2\), Definite quadratic forms over \({\mathbb F}_q[x\)], The lens space realization problem, Some remarks on units in Grothendieck-Witt rings, Quadratic forms and quadrics of space over local rings, \(K\)-Witt bordism in characteristic 2, On intersection forms of definite 4-manifolds bounded by a rational homology 3-sphere, Positive definite lattices of rank at most 8., Free loop space homology of highly connected manifolds, Endomorphism rings of abelian surfaces and projective models of their moduli spaces, Splitting the concordance group of algebraically slice knots, Partition functions for heterotic WZW conformal field theories., Pieces of eight: semiselfdual lattices and a new foundation for the theory of Conway and Mathieu groups, A shadow identity and an application to isoduality., A few weight systems arising from intersection graphs, Equality of orthogonal transvection group and elementary orthogonal transvection group, Jacobian tori associated with a finite graph and its abelian covering graphs, Non-orientable surfaces in 3-manifolds, Witt rings of fields of quotients of two-dimensional regular local rings, Enumeration of quadrics of projective spaces over local rings, Homotopy groups of certain highly connected manifolds via loop space homology, A quick proof of reciprocity for Hecke Gauss sums, Analysis of DeepBKZ reduction for finding short lattice vectors, Quantum invariants at the sixth root of unity, A cancellation theorem for projective modules in the metastable range, Corollaries of the A-H-V formula, Eisenstein formula and Dirichlet correspondence, Cohomologische Invarianten quadratischer Formen, The rational homotopy type of configuration spaces of two points., Jacobians isomorphic to a product of two elliptic curves and ternary quadratic forms, On algebraic curves over real closed fields. I, Superpythagorean fields, Representations of integral quadratic forms by sums of squares, Bilinear and quadratic forms on torsion modules, Hasse-Witt invariants for (\(\alpha u\))-reflexive forms and automorphisms. I: Algebraic \(K_2\)-valued Hasse-Witt invariants, Codes correcteurs d'erreurs autoorthogonaux sur le corps à deux éléments et formes quadratiques entières definies positives à discriminant +1, Stabile Modulformen, Homotopy groups of highly connected manifolds, Cayley algebras and the isomorphisms of the orthogonal groups over arithmetic and local domains, The orthogonal group over a full ring, A calculus for framed links in \(S^3\), Adjunctions in monoidal categories, Frobenius algebras and hermitian forms, On the description of the reduced Witt ring, Some remarks concerning matrices of the form \(A-A'\), \(A^{-1}A'\), Homotopy classification of some four-dimensional manifolds, Computations of Witt groups of finite groups, Homogeneous vector bundles and families of Calabi-Yau threefolds, Symplectic fillings and positive scalar curvature, Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\). II: Application of \(K\)-convexity, Classification of the rational Seifert forms of plane curve germs, A note on optimal unimodular lattices, Microlocal analysis and calculations on some relatively invariant hyperfunctions related to zeta functions associated with the vector spaces of quadratic forms, A relation of primal--dual lattices and the complexity of shortest lattice vector problem, Hermitian K-theory over topological *-algebras, The shadow theory of modular and unimodular lattices, Grids and the arithmetics of Jordan pairs, A strong coupling test of \(S\)-duality, New complex- and quaternion-hyperbolic reflection groups, Gitter ohne Automorphismen der Determinante -1, 4-manifolds \(X\) over \(BS\text{U}(2)\) and the corresponding homotopy types Map\((X,BS\text{U}(2))\), Comparing Witt rings, Grothendieck and Witt groups of orders and finite groups, On certain Mordell-Weil lattices of hyperelliptic type on rational surfaces, \(p\)-adic Heisenberg group and Maslov index, Graphs with least eigenvalue \(-2\); a historical survey and recent developments in maximal exceptional graphs, Automorphisms of even unimodular lattices and unramified Salem numbers, A new transference theorem in the geometry of numbers and new bounds for Ajtai's connection factor, On geometrical interpretation of the \(p\)-adic Maslov index, Self-adjoint determinantal representations of real plane curves, New bounds in some transference theorems in the geometry of numbers, On the computation of the projective surgery obstruction groups, Quaternion lattices and Venkov invariant., Cohomologically generic 2-complexes and 3-dimensional Poincaré complexes, Which 4-manifolds are toric varieties?, An intrinsic Arf invariant on a link and its surface-link analogue, EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS, THE ZEROTH -STABLE HOMOTOPY SHEAF OF A MOTIVIC SPACE, Unnamed Item, A mass formula for unimodular lattices with no roots, Unnamed Item, Inner products and ℤ/p, A Gersten–Witt spectral sequence for regular schemes, All frame-spun knots are slice, Unnamed Item, Unnamed Item, Remarks on classical number-theoretic aspects of Milnor–Witt K-theory, The nonexistence of certain tight spherical designs, Unnamed Item, Unnamed Item, The geography problem for 4-manifolds with specified fundamental group, Igusa-type functions associated to finite formed spaces and their functional equations, Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds, ON INTEGERS OCCURRING AS THE MAPPING DEGREE BETWEEN QUASITORIC 4-MANIFOLDS, Unnamed Item, Unnamed Item, On the Topological Structure of Even-Dimensional Complete Intersections, Unnamed Item, Exceptional collections in surface-like categories, Distinguishing $$G_2$$-Manifolds, Witt equivalence of function fields over global fields, Motivic and real étale stable homotopy theory, TOWER FORMULA FOR DISCRIMINANT, The Poincaré Conjecture and Related Statements, $\Lambda $-sphères, Logarithmes des points rationnels des variétés abéliennes, On a Waring’s problem for integral quadratic and Hermitian forms, Witt classes of integral representations of an Abelian $p$-group, Witt equivalence of fields: A survey with a special emphasis on applications of hyperfields, Localisation de formes quadratiques $I$, Unnamed Item, Hermitian periodicity and cohomology of infinite orthogonal groups, Group Representations and Lattices, Local surgery and applications to the theory of quadratic forms, Clifford quantum cellular automata: Trivial group in 2D and Witt group in 3D, Heegaard Floer invariants in codimension one, Formes quadratiques d'enlacement sur l'anneau des entiers d'un corps de nombres, Witt equivalence of function fields of conics, Real algebraic curves, A classification theorem for Albert algebras, Localisation de formes quadratiques. II, Failure of a quadratic analogue of Serre’s conjecture, On the classification and enumeration of self-dual codes, On the cokernel of the Witt decomposition map, The strongly perfect lattices of dimension 10, Invariants of a quadratic form attached to a tame covering of schemes., Some estimations in the topology of simply-connected algebraic surfaces, On natural homomorphisms of Witt rings, On existence of tame Harrison map, Hermite’s Constant and Lattice Algorithms, $R$-equivalence in adjoint classical groups over fields of virtual cohomological dimension $2$, The smallest hyperbolic 6-manifolds, Spin Borromean surgeries, Witt rings of Hasse domains of global fields, An Étale realization which does NOT exist, Real representatives of equisingular strata of simple quartic surfaces, Incoherent Definite Spaces and Shimura Varieties, Hollow polytopes of large width, Characteristic fixed-point sets of semifree actions on spheres, On compact representations of Voronoi cells of lattices, Unnamed Item, On the lattice of polynomials with integer coefficients: successive minima in $L_2(0,1)$, Imbedding four-manifolds and slicing links, Unnamed Item, Rational points and non-anticanonical height functions, The Witt group of real algebraic varieties, The Boolean Space of Orderings of a Field, Imbedding four-manifolds and slicing links, Unnamed Item, Realizing doubles: a conjugation zoo, Remarques sur la forme trace, Quantum Codes from High-Dimensional Manifolds, Eine charakterisierung der reelen abschlüsse von semilokalen ringen, Bilinear-form invariants of Lefschetz fibrations over the 2-sphere, Some Results on Orientation Preserving Involutions, Linear hyperbolic systems on networks: well-posedness and qualitative properties, Generalized line graphs, Arithmetic invariant theory, Four-dimensional topology: an introduction, HIGHER -THEORY OF FORMS I. FROM RINGS TO EXACT CATEGORIES, Branched coverings of CP2 and other basic 4‐manifolds, On a real places of a field and their holomorphy ring, Unnamed Item, Unnamed Item, Haar Measure and the Artin Conductor, Weil Representation and Metaplectic Groups over an Integral Domain, Linking forms, reciprocity for Gauss sums and invariants of 3-manifolds, Determining the Trisection Genus of Orientable and Non-Orientable PL 4-Manifolds through Triangulations, Stability in Witt Rings, Alternating and symmetric multilinear forms and poincaré algebras, Root lattices in number fields, The Reduced Witt Ring of a Formally Real Field, Bilinear forms and cyclic group actions, Topological models for stable motivic invariants of regular number rings, Linking Forms and Maps of Odd Prime Order, On global singularities of Sobolev mappings, Hyperbolic posets and homology stability for \(O_{n,n}\), Abelian quotients of mapping class groups of highly connected manifolds, Inhomogeneous minima of mixed signature lattices, Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields, Elementary transformations of Dynkin graphs and singularities on quartic surfaces, On bilinear forms of height 2 and degree 1 or 2 in characteristic 2, Even unimodular 12-dimensional quadratic forms over \({\mathbb{Q}}(\sqrt{5})\), The Hasse principle for bilinear symmetric forms over a ring of integers of a global function field, The Weil representation and Hecke operators for vector valued modular forms, Products of quasireflections and transvections over local rings, On the injectivity of the map of the Witt group of a scheme into the Witt group of its function field, On splitting the Knebusch-Milnor exact sequence, Witt groups of algebraic integers, On the conformal systoles of four-manifolds, Exceptional collections, and the Néron-Severi lattice for surfaces, Tie transformations of Dynkin graphs and singularities on quartic surfaces, Involutions on odd four-manifolds, Minima, slopes and tensor algebra, Spaces of orderings and Witt rings of planar ternary rings, Class numbers of quadratic fields and Shimura's correspondence, Some examples related to knot sliceness, Weil representations associated with finite quadratic modules, Branched covers of surfaces in 4-manifolds, New transference theorems on lattices possessing \(n^\varepsilon\)-unique shortest vectors, Rational analogs of projective planes, New invariants of \(G_{2}\)-structures, Algebraic classification of linking pairings on 3-manifolds, Hermitian \(K\)-theory and 2-regularity for totally real number fields, Invariants mod-2 and subgroups of \(G_2\) and \(F_4\), The Witt ring of a full ring, Discrete subgroups acting transitively on vertices of a Bruhat-Tits building, Topology of nonsingular complex hypersurfaces, Wu invariants of Hermitian forms, Rational Witt classes of Pretzel knots, Some exact sequences in the theory of Hermitian forms, Sets with many pairs of orthogonal vectors over finite fields, The orthogonal and the special orthogonal groups over a full ring, Concordance classes of regular O(n)-actions on homotopy spheres, The surgery obstruction groups for finite 2-groups, Stabilizers of subspaces under similitudes of the Klein quadric, and automorphisms of Heisenberg algebras, Quadratic forms and Artin's reciprocity law, On the local theory of signatures and reduced quadratic forms, Quaternionic skew-hermitian forms over a number field, New improved exact sequences of Witt groups, Fibre de Milnor d'un cône sur une courbe plane singulière, A construction for integral symmetric bilinear forms, Die Wirkung von Heckeoperatoren auf Thetareihen mit harmonischen Koeffizienten, The isometry classification of Hermitian forms over division algebras, Hecke's theorem in quadratic reciprocity, finite nilpotent groups and the Cooley-Tukey algorithm, The unimodular lattices of dimension up to 23 and the Minkowski-Siegel mass constants, Equivariant K-theory and forms over twisted group rings, Definite hermitian forms and the cancellation of simple knots, Symmetric bilinear forms, quadratic forms and Milnor K-theory in characteristic two, Wittringe höherer Stufe, A modified Stiefel-Whitney invariant and a calculation in \(K_ 3 \)of an algebraic number field, Branched coverings of simply connected manifolds, Good bilinear and quadratic forms of height 2 in characteristic 2., The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl\((2,\mathbb{C})\), On lattices over valuation rings of arbitrary rank, On binary integral quadratic forms having isometric groups of automorphisms, A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula, High, low, and quantitative roads in linear algebra, A \(p\)-adic approach to the Weil representation of discriminant forms arising from even lattices, A fast isomorphism test for groups whose Lie algebra has genus 2, A normal form and schemes of quadratic forms, Hermitian \(K\)-theory, derived equivalences and Karoubi's fundamental theorem, Designs as maximum codes in polynomial metric spaces, Rational homology of the group \(\text{O}_n(\mathbb{Z}[\tfrac 12)\) and automorphisms of unimodular lattices], On braided fusion categories. I, Witt kernels of function field extensions in characteristic 2, Isotropy of an Albert bilinear form over the function field of a quadric in characteristic 2, Aspects of group actions on four-manifolds, Equivariant Gauss sum of finite quadratic forms, Weyl groups, lattices and geometric manifolds., The overarching finite symmetry group of Kummer surfaces in the Mathieu group \(M_{24}\), Cocyclic Hadamard matrices from forms over finite Frobenius rings, The concordance genus of a knot. II., On a type of commutative algebras, On spectral characterization and embeddings of graphs, Über rationale Homologiesphären, Singular elements and the Witt equivalence of rings of algebraic integers, Fields of 2-planes and two kinds of almost complex structures on compact 4-dimensional manifolds, Definite lattices over real algebraic function domains, A Hermitian analog of a quadratic form theorem of Springer, Orientation reversal of manifolds, Sphere packing, Discrete hyperbolic geometry, Instantons and the topology of 4-manifolds, A Hermitian Morita theorem for algebras with anti-structure, Theta series of a real algebraic number field, Topological properties of certain incomplete regular intersections, Eine Kongruenz für Gitter und ihre Anwendung auf 2k-Mannigfaltigkeiten in 4k-Mannigfaltigkeiten, The Witt classes of torsion linking forms of (4n-1)-manifolds with pseudo-free circle actions, A converse to the P. A. Smith theorem for nonunitary homology spheres, Symplectic \(K_ 2\) of Laurent polynomials, associated Kac-Moody groups and Witt rings, Trace forms of dyadic number fields, Quadratic forms and the graph isomorphism problem, Infinite-dimensional Lie algebras, theta functions and modular forms, Rohlin's invariant and gauge theory III. Homology \(4\)--tori, The geometric distribution of Selmer groups of elliptic curves over function fields, Natural homomorphism of Witt rings of a certain cubic order, Saint Petersburg school of the theory of linear groups. I: Prehistory, The elliptic sieve and Brauer groups, Equivariant 4‐genera of strongly invertible and periodic knots, η$\eta$‐Periodic motivic stable homotopy theory over Dedekind domains, Most odd-degree binary forms fail to primitively represent a square, From zero surgeries to candidates for exotic definite 4‐manifolds, Fermionic CFTs from classical codes over finite fields, Finite quadratic modules and lattices, A refined scissors congruence group and the third homology of \(\operatorname{SL}_2\), Matrix Kloosterman sums modulo prime powers, Unnamed Item, Unnamed Item, On Inner Product Spaces Over Dedekind Domains of Characteristic Two, The complex hyperbolic geometry of the moduli space of cubic surfaces, On the Tits indices of absolutely almost simple algebraic groups over local and global fields, Symplectic mapping class groups of K3 surfaces and Seiberg-Witten invariants, Lattice reduction with approximate enumeration oracles. Practical algorithms and concrete performance, Transfer for Kato-Milne cohomology over purely inseparable extensions (with an appendix by Diksha Mukhija), On the non-amenability of the reflective quotient, Automorphisms of projective K3 surfaces with minimum entropy, Bak's work on theK-theory of rings, Stretching and welding indecomposable quadratic forms, Counting lattice vectors, Siegel modular forms of weight 13 and the Leech lattice, The concordance crosscap number and rational Witt span of a knot, Unnamed Item, Galois conjugation and multiboundary entanglement entropy, Cdh descent, cdarc descent, and Milnor excision, K-theory of real algebraic surfaces and threefolds, Quadratic Forms and the Birman-Craggs Homomorphisms, Unnamed Item, Topology through the centuries: Low dimensional manifolds, A new upper bound for the minimum of an integral lattice of determinant 1, On the characterization of rational homotopy types and Chern classes of closed almost complex manifolds, Witt invariants from \(q\)-series \(\hat{Z}\), Heterotic strings on \(\mathbb{T}^3/\mathbb{Z}_2\), Nikulin involutions and M-theory, Nontrivial quantum cellular automata in higher dimensions, A construction of antisymmetric modular forms for Weil representations, Counterexamples in 4-manifold topology, Eisenstein's program and modular forms, Cohomologie de Galois et cohomologie des variétés algébriques réelles ; applications aux surfaces rationnelles, Orthogonal decompositions of integral trace forms of cyclotomic fields and their canonical forms over the ring of \(p\)-adic integers, A TRACE FORMULA FOR HECKE OPERATORS ON VECTOR-VALUED MODULAR FORMS, Lifting problem for universal quadratic forms, Group cohomology and gauge equivalence of some twisted quantum doubles, SL-oriented cohomology theories, Lectures on Chow-Witt groups, Relations in \(I^{n}\) and \(I^{n}W_{q}\) in characteristic 2, Homotopy classification of maps between simply connected four manifolds, Positive definite \(n\)-regular quadratic forms, Characterisation of homotopy ribbon discs, Maximality of orders in Dedekind domains, Rings of integers in number fields and root lattices, Homotopy classes of rational functions, Remarks on a certain idempotency property of witt rings, An application of Siegel's formula over quaternion orders, A construction of integral lattices, Witt equivalence of semilocal Dedekind domains in global fields, Trace maps for Mackey algebras, A link invariant with values in the Witt ring, Obstruction theory for the approximation and the deformation problems for Sobolev mappings, Split states, entropy enigmas, holes and halos, A Bezoutian approach to orthogonal decompositions of trace forms or integral trace forms of some classical polynomials, Signatures on semilocal rings, Relative Rochlin invariants, Dynamics on K3 surfaces: Salem numbers and Siegel disks, Minima and slopes of rigid adelic spaces, Euclidean lattices, theta invariants, and thermodynamic formalism, Quadratic Forms, Witt vectors. Part 1, Espaces quadratiques sur un anneau regulier, Free partition functions and an averaged holographic duality, Réseaux unimodulaires, On the cohomology of the classifying space of the gauge group over some 4-complexes, A presentation of the group \(\text{Sl}_*(2,A)\), \(A\) a simple Artinian ring with involution., Geometric cycles and characteristic classes of manifold bundles (with an appendix by M. Krannich), IIB flux non-commutativity and the global structure of field theories, Twisted component sums of vector-valued modular forms, Siegel theta series for indefinite quadratic forms, Real intersection homology. II: A local duality obstruction, Maximality of orders in Dedekind domains. II, On complex surfaces with definite intersection form, Two-Forms on Four-Manifolds, From Goeritz Matrices to Quasi-alternating Links, Slopes of Euclidean lattices, tensor product and group actions, The descent of biquaternion algebras in characteristic two, A classical proof that the algebraic homotopy class of a rational function is the residue pairing, Intersection homology with field coefficients:K-Witt spaces andK-Witt bordism, Jacobson’s theorem for bilinear forms in characteristic 2, Flat connections and resonance varieties: From rank one to higher ranks, Diffeomorphic complete intersections with different multidegrees, \(\mathbb{A}^1\)-homotopy theory and contractible varieties: a survey, Ein Teilformensatz für quadratische Formen in Charakteristik 2, Pieces of \(2^d\)\,: existence and uniqueness for Barnes-Wall and Ypsilanti lattices, Twisted Blanchfield pairings and twisted signatures. I: algebraic background, Symplectic and orthogonal \(K\)-groups of the integers, Bilinear forms of dimension less than or equal to 5 and function fields of quadrics in characteristic 2, Monoids of linking pairings and orthogonal summands, Closed manifolds coming from Artinian complete intersections, Motivic stable homotopy theory is strictly commutative at the characteristic, On the splitting principle for cohomological invariants of reflection groups, The unknotting number and classical invariants. I, There is no Enriques surface over the integers, Hermitian K-theory via oriented Gorenstein algebras, Discriminants in characteristic two, Normal Forms for Definite Integer Unimodular Quadratic Forms, Functorial seminorms on singular homology and (in)flexible manifolds, An analogue of a result of Tits for transvection groups, From deep holes to free planes, Bounds on the lattice point enumerator via slices and projections, A theory of concordance for non-spherical 3-knots, Real cohomology and the powers of the fundamental ideal in the Witt ring
