Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92)

cobordism characteristic classes integrality Bockstein spectral sequence infinite loop space theory delooping bordism rings of piecewise linear and topological manifolds classifying space for topological sphere bundles away from 2 cohomology of BPL and BTOP G/TOP mod 2 spherical characteristic classes PL genus relations involving Milnor manifolds simply connected surgery

Mathematics Subject Classification ID

Sphere bundles and vector bundles in algebraic topology (55R25) Stable classes of vector space bundles in algebraic topology and relations to (K)-theory (55R50) Classifying spaces of groups and (H)-spaces in algebraic topology (55R35) Surgery and handlebodies (57R65) Homology of classifying spaces and characteristic classes in algebraic topology (55R40) Spectral sequences in algebraic topology (55T99) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02) Infinite loop spaces (55P47) Surgery obstructions, Wall groups (57R67) Research exposition (monographs, survey articles) pertaining to algebraic topology (55-02) Eilenberg-Moore spectral sequences (55T20) Applications of Eilenberg-Moore spectral sequences (57T35) Homology and cohomology of (H)-spaces (57T25) Cobordism and concordance in topological manifolds (57N70) Cobordism and concordance in PL-topology (57Q60) Cobordism in PL-topology (57Q20)

Related Items

L‐theory of C∗$C^*$‐algebras, Equivariant Gysin maps and pulling back fixed points, Characteristic classes of Galois representations, The cohomology of the Sylow 2-subgroup of the Higman-Sims group, The cohomology of the Steenrod algebra and representations of the general linear groups, Toward the group completion of the Burau representation, Inertia groups and smooth structures on quaternionic projective spaces, Topological finiteness theorems for manifolds in Gromov-Hausdorff space, Homotopical dynamics IV. Hopf invariants and Hamiltonian flows, Homotopy of gauge groups over non-simply-connected five-dimensional manifolds, Smooth manifolds with prescribed rational cohomology ring, Extended Dyer-Lashof algebras and modular coinvariants, A note on group actions on homology spheres, Steenrod operations on the modular invariants, Modular Symbols and the Topological Nonrigidity of Arithmetic Manifolds, Vector bundles with infinitely many souls, On the extended crystal PDE's stability. I: The $n$-d'Alembert extended crystal PDE's, On the extended crystal PDE's stability. II: Entropy-regular-solutions in MHD-PDE's, On bundles that admit fiberwise hyperbolic dynamics, Group actions on homology spheres, Toward a Galois theory of the integers over the sphere spectrum, The Novikov conjecture for linear groups, Classifying seven dimensional manifolds of fixed cohomology type, On the classification of G-spheres. I. Equivariant transversality, Regular circle actions on 2-connected 7-manifolds, One-connectivity and finiteness of HamiltonianS¹-manifolds with minimal fixed sets, Moduli space of non-negative sectional or positive Ricci curvature metrics on sphere bundles over spheres and their quotients, Higher operations in string topology of classifying spaces, Positive scalar curvature for manifolds with elementary abelian fundamental group, Dualizing spheres for compact $p$-adic analytic groups and duality in chromatic homotopy, The Gromoll filtration, $KO$-characteristic classes and metrics of positive scalar curvature, Mod-two cohomology rings of alternating groups, A survey of bordism and cobordism, Quantum extended crystal super PDEs, Rational models for automorphisms of fiber bundles, Rational analogs of projective planes, On the cardinality of the manifold set, Rigid cyclic group actions on cohomology complex projective spaces, The rational stable homology of mapping class groups of universal nil-manifolds, Unnamed Item, Bordism groups of fold maps, Surgery and bordism groups in quantum partial differential equations. I: The quantum Poincaré conjecture, Surgery and bordism groups in quantum partial differential equations. II: Variational quantum PDEs, A classification of $S^{3}$-bundles over $S^{4}$, Counterexamples in 4-manifold topology, Obstructions to stably fibering manifolds, Relations in the piecewise-linear cobordism ring, Fonctorialité en K-théorie bivariante pour les variétés lipschitziennes. (Functoriality in the bivariant K-theory for Lipschitz manifolds), Topological gauge theories and group cohomology, Topological triviality of smoothly knotted surfaces in $4$-manifolds, The smooth Whitehead spectrum of a point at odd regular primes, Orientable $4$-dimensional Poincaré complexes have reducible Spivak fibrations, On the contribution of Wu Wen-Tsün to algebraic topology, Curvature, tangentiality, and controlled topology, Characterisation of homotopy ribbon discs, Differential KO-theory: constructions, computations, and applications, On smoothable surgery for 4-manifolds, Generalized manifolds, normal invariants, and 𝕃-homology, The Action of the Steenrod Squares on the Modular Invariants of Linear Groups, A center transversal theorem for an improved Rado depth, On the relation between K- and L-theory of $C^*$-algebras, Cohomology of Metacyclic Groups, The image of the map from group cohomology to Galois cohomology, The additivity of the $\rho $-invariant and periodicity in topological surgery, Smooth varieties up to $\mathbb A^1$-homotopy and algebraic $h$-cobordisms, Construction d'éléments dans $\pi^S_*(BU(2))$, Bordism of semi-free $S^1$-actions, Pseudoisotopies and the Bökstedt trace, On free ${\mathbb{Z}_{p}}$ actions on products of spheres, The smooth structure set of $S^{p} \times S^{q}$, Codimension two souls and cancellation phenomena, Spin${}^h$ and further generalisations of spin, Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology, On highly regular embeddings, Note on the existence of almost complex structures on compact manifolds, Non-aspherical ends and non-positive curvature, The Iterated Total Squaring Operation, Modular coinvariants and the modphomology ofQS^k, On fake Lens spaces with fundamental group of order a power of 2, Additive Cohomology Operations, Extended crystal PDE's stability. I: The general theory, Extended crystal PDE'S stability, II: The extended crystal MHD-PDE'S, Higher simple structure sets of lens spaces with the fundamental group of arbitrary order, Finite group actions on Kervaire manifolds, On 1-connected 8-manifolds with the same homology as $S^3\times S^5$, (Co)bordism groups in quantum super PDEs. II: Quantum super PDEs, The mod-p cohomology rings of metacyclic groups, Exotic characteristic classes and their relation to universal surgery classes, Higher simple structure sets of Lens spaces with the fundamental group of order $2^K$, Realizing characteristic classes by manifolds, Symmetric invariants and cohomology of groups, Relations among smooth Kervaire classes and smooth involutions on homotopy spheres, Correction to: ``Moduli spaces of nonnegative sectional curvature and non-unique souls, Kreck-Stolz invariants for quaternionic line bundles, Homology operations in G/TOP, Topological nonrigidity of nonuniform lattices, Some finiteness results for groups of automorphisms of manifolds, Cohomology and group actions, Tangential thickness of manifolds, Invariants of fold-maps via stable homotopy groups, Semicharacteristics, Bordism, and Free Group Actions, Homotopy-theoretically enriched categories of noncommutative motives, On the Structure of Finite Groups with Periodic Cohomology, Polynomial operations on complex K-theory, Relations of smooth Kervaire classes over the mod 2 Steenrod algebra, Topologically invariant integral characteristic classes