منابع مشابه
Intersection Homology Theory
INTRODUCTION WE DEVELOP here a generalization to singular spaces of the Poincare-Lefschetz theory of intersections of homology cycles on manifolds, as announced in [6]. Poincart, in his 1895 paper which founded modern algebraic topology ([18], p. 218; corrected in [19]), studied the intersection of an i-cycle V and a j-cycle W in a compact oriented n-manifold X, in the case of complementary dim...
متن کاملHomology stratifications and intersection homology
A homology stratification is a filtered space with local homology groups constant on strata. Despite being used by Goresky and MacPherson [3] in their proof of topological invariance of intersection homology, homology stratifications do not appear to have been studied in any detail and their properties remain obscure. Here we use them to present a simplified version of the Goresky–MacPherson pr...
متن کاملPersistent Intersection Homology
The theory of intersection homology was developed to study the singularities of a topologically stratified space. This paper incorporates this theory into the already developed framework of persistent homology. We demonstrate that persistent intersection homology gives useful information about the relationship between an embedded stratified space and its singularities. We give, and prove the co...
متن کاملIntersection Homology II
In [19, 20] we introduced topological invariants IH~,(X) called intersection homology groups for the study of singular spaces X. These groups depend on the choice of a perversity p: a perversity is a function from {2, 3, ...} to the non-negative integers such that both /~(c) and c 2 / ~ ( c ) are positive and increasing functions of c (2.1). The group IHr is defined for spaces X called pseudoma...
متن کاملIntersection homology Künneth theorems
Cohen, Goresky and Ji showed that there is a Künneth theorem relating the intersection homology groups I H∗(X × Y ) to I H∗(X) and I H∗(Y ), provided that the perversity p̄ satisfies rather strict conditions. We consider biperversities and prove that there is a Künneth theorem relating I H∗(X × Y ) to I H∗(X) and I H∗(Y ) for all choices of p̄ and q̄. Furthermore, we prove that the Künneth theorem...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology
سال: 1980
ISSN: 0040-9383
DOI: 10.1016/0040-9383(80)90003-8