Intersection Homology
DOI10.1007/978-3-030-78024-1_5zbMath1486.14002OpenAlexW4211194481MaRDI QIDQ5024551
Publication date: 26 January 2022
Published in: Handbook of Geometry and Topology of Singularities II (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-030-78024-1_5
Singularities in algebraic geometry (14B05) Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) (32S60) Poincaré duality spaces (57P10) Research exposition (monographs, survey articles) pertaining to algebraic topology (55-02) Algebraic and analytic properties of mappings on manifolds (58K20) Intersection homology and cohomology in algebraic topology (55N33) Derived categories, triangulated categories (18G80)
Cites Work
- Localized intersection of currents and the Lefschetz coincidence point theorem
- Steenrod squares on intersection cohomology and a conjecture of M. Goresky and W. Pardon
- Foliated stratified spaces and a de Rham complex describing intersection space cohomology
- Cup and cap products in intersection (co)homology
- \(L^{\infty}\) cohomology is intersection cohomology
- On the geometry of polynomial mappings at infinity
- \(L^ 2\)-cohomology of normal algebraic surfaces. I
- Hard Lefschetz theorem for nonrational polytopes
- Intersection homology with general perversities
- Equivariant intersection cohomology of the circle actions
- L\({}_ 2\)-cohomology of arithmetic varieties
- Algebraic geometry and analytic geometry
- Les singularités des applications différentiables
- Intersection homology. II
- \(L^ 2\)-cohomology and intersection homology of stratified spaces
- Intersection homology operations
- Intersection cohomology. (Notes of a Seminar on Intersection Homology at the University of Bern, Switzerland, Spring 1983)
- Cheeger-Goreski-MacPherson's conjecture for the varieties with isolated singularities
- Theorème de De Rham pour les variétés stratifiées. (The De Rham theorem for stratified manifolds)
- De Rham intersection cohomology for general perversities
- Stratified Morse theory: past and present
- Remarks on the combinatorial intersection cohomology of fans
- Wu numbers of singular spaces
- Intersection spaces, spatial homology truncation, and string theory
- Intersection homology Künneth theorems
- Intersection homology and Poincaré duality on homotopically stratified spaces
- Topological invariance of intersection homology without sheaves
- Elementary construction of perverse sheaves
- Lefschetz fixed point theorem for intersection homology
- \(L^ 2\) and intersection cohomologies for a polarizable variation of Hodge structure
- \(L_ 2\)-cohomology and intersection homology of certain algebraic varieties with isolated singularities
- The Poincaré lemma for variations of polarized Hodge structure
- Vanishing of odd-dimensional intersection cohomology
- Intersection homology of toric varieties and a conjecture of Kalai
- The number of faces of a simplicial convex polytope
- Hodge theory with degenerating coefficients: \(L_2\) cohomology in the Poincaré metric
- Intersection homology theory
- Intersection cohomology of cs-spaces and Zeeman's filtration
- Singular spaces, characteristic classes, and intersection homology
- Weights of exponential sums, intersection cohomology, and Newton polyhedra
- \(\mathcal L^ 2\)-cohomologie des espaces stratifiés. (\(\mathcal L^ 2\)- cohomology of stratified spaces)
- On the \(L^ 2\) cohomology of complex spaces
- \(L_ 2\)-cohomology of Kähler varieties with isolated singularities
- Local contribution to the Lefschetz fixed point formula
- Density of Morse functions on a complex space
- \(L^ p\) cohomology of cones and horns
- Sheaves in topology
- Sur l'analysis situs des variétés à \(n\) dimensions
- Combinatorial intersection cohomology for fans.
- A complex in Morse theory computing intersection homology
- Real intersection homology
- Poincaré duality with cap products in intersection homology
- A Lefschetz coincidence theorem for singular varieties
- On singular varieties associated to a polynomial mapping from \(\mathbb{C}^n\) to \(\mathbb{C}^{n-1}\)
- Intersection cohomology of reductive varieties
- Remarks on the \(L^ 2\)-cohomology of singular algebraic surfaces
- L//2 cohomology of warped products and arithmetic groups
- Intersection homology and homology manifolds
- Lifting of algebraic cycles and associated homomorphisms in intersection homology.
- Local and global coincidence homology classes
- A Lefschetz duality for intersection homology
- Hodge theory for intersection space cohomology
- Intersection cohomology of the circle actions
- Intersection homology: general perversities and topological invariance
- Intersection differential forms
- The numbers of faces of simplicial polytopes
- Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
- Intersection theory on toric varieties
- Combinatorial duality and intersection product: a direct approach
- Superperverse intersection cohomology: stratification (in)dependence
- Homology theory for locally compact spaces
- Sur quelques points d'algèbre homologique
- Homology with local coefficients
- Introduction to Toric Varieties. (AM-131)
- Rational intersection cohomology of projective toric varieties.
- Differential Forms On Regular Affine Algebras
- Witt Spaces: A Geometric Cycle Theory for KO-Homology at Odd Primes
- Singular chain intersection homology for traditional and super-perversities
- The decomposition theorem, perverse sheaves and the topology of algebraic maps
- Espaces de Thom et contre-exemples de J.L. Verdier et M. Goresky
- Morse Theory. (AM-51)
- Sufficiency of McMullen’s conditions for 𝑓-vectors of simplicial polytopes
- Categorical framework for the study of singular spaces
- $L^2 - \overline \partial$-Cohomology of Complex Projective Varieties
- Simplicial Differential Forms with Poles
- On the Kunneth Formula for Intersection Cohomology
- On the spectral geometry of spaces with cone-like singularities
- Differential forms on singular varieties and cyclic homology
- On the Hodge theory of stratified spaces
- Intersection Cohomology. Simplicial Blow-up and Rational Homotopy
- Blown-up intersection cohomology
- Shadow Forms of Brasselet-Goresky-MacPherson
- Towards a combinatorial intersection cohomology for fans
- Cobordism of maps of locally orientable Witt spaces
- Categories and Sheaves
- ON A SINGULAR VARIETY ASSOCIATED TO A POLYNOMIAL MAPPING
- A generalized lower‐bound conjecture for simplicial polytopes
- Vanishing of odd dimensional intersection cohomology. II
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