In topology, a branch of mathematics, intersection homology is an analogue of singular homology especially well-suited for the study of singular spaces...

Borel–Moore homology Cellular homology Cyclic homology Hochschild homology Floer homology Intersection homology K-homology Khovanov homology Morse homology Persistent...

solutions of holonomic D-modules. A key observation was that the intersection homology of Mark Goresky and Robert MacPherson could be described using sheaf...

In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is a novel invariant that arises...

In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1 {\displaystyle n\geq 1} ...

Kari Vilonen, and Zhiwei Yun. MacPherson and Goresky introduced intersection homology. He also worked on arithmetic groups, in particular on Siegel modular...

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated...

singular varieties is provided by intersection homology. Namely, Morihiko Saito showed that the intersection homology of any complex projective variety...

Robert Mark Goresky is a Canadian mathematician who invented intersection homology with his advisor and life partner Robert MacPherson. Goresky received...

intersections induces an isomorphism C i M → C n − i M {\displaystyle C_{i}M\to C^{n-i}M} , where C i {\displaystyle C_{i}} is the cellular homology of...

(co)homology groups of the whole space, the direct sum of the (co)homology groups of the subspaces, and the (co)homology groups of the intersection of...

In mathematics, the intersection form of an oriented compact 4-manifold is a special symmetric bilinear form on the 2nd (co)homology group of the 4-manifold...

sequence Gauss–Manin connection D-module Intersection homology Perverse sheaf Steenrod, Norman E. (1943). "Homology with local coefficients". Annals of Mathematics...

Hochschild homology (and cohomology) is a homology theory for associative algebras over rings. There is also a theory for Hochschild homology of certain...

algebra, in particular for his classic papers on singular homology and his work on axiomatic homology theory which had a profound influence on the development...

stratification Flattening stratification Appendix 1 of R. MacPherson, Intersection homology and perverse sheaves, 1990 notes J. Mather, Stratifications and...

Contact (mathematics) Singular solution Stratification (mathematics) Intersection homology Mixed Hodge structure Whitney umbrella Round function Victor Goryunov...

Goresky, L2 cohomology is intersection cohomology Frances Kirwan, Jonathan Woolf An Introduction to Intersection Homology Theory,, chapter 6 ISBN 1-58488-184-4...

prime spectrum. Singularity theory Whitney conditions Stratifold Intersection homology Thom's first isotopy lemma stratified space Goresky, Mark; MacPherson...

technical complexities used to demonstrate more complex theory, such as intersection homology and perverse sheaves. This family is given by W = { ( t , x , y...

University Press. 1984. ISBN 978-0691083704. An Introduction to Intersection Homology Theory. Longman Scientific and Technical. 1988. with Jonathan Woolf:...

boundary homomorphism is given by ∂D = 2C1 and ∂C1 = ∂C2 = 0, yielding the homology groups of the Klein bottle K to be H0(K, Z) = Z, H1(K, Z) = Z×(Z/2Z) and...

Smoothness, Regularity and Complete Intersection. Cambridge University Press. ISBN 9781139107181. Tate, John (1957), "Homology of Noetherian rings and local...

mathematics, an algebraic variety V in projective space is a complete intersection if the ideal of V is generated by exactly codim V elements. That is,...

homology theory using Lagrangian intersection Floer homology, which they conjecture to be isomorphic to a singly graded version of Khovanov homology....

and the Topology of Algebraic Maps (PDF) MacPherson, R. (1990). "Intersection homology and perverse sheaves" (PDF). Hotta, Ryoshi; Takeuchi, Kiyoshi; Tanisaki...

perturb Poincaré duality". This in turn led to the discovery of intersection homology by Robert MacPherson and Mark Goresky at Brown University where...

positive characteristic. The theorem can also be generalized to intersection homology. In this setting, the theorem holds for highly singular spaces....

means: take the complex IC of sheaves whose hyperhomology is the intersection homology of the Schubert variety of w (the closure of the cell Xw), take...

D from Brown University under Robert MacPherson with thesis The Intersection Homology D-module on Hypersurfaces with Isolated Singularities. From 1983...