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A multiperversity generalization of intersection homology. (English) Zbl 1160.55004

The intersection homology groups for stratified spaces \(X\), as introduced by M. Goresky and R. MacPherson [Topology 19, 135–165 (1980; Zbl 0448.55004)] depend on certain sequences of integers called perversities, which describe how simplicies are allowed to intersect in the singular set of \(X\). The authors introduce a generalization of intersection homology based on a set of perversities, which tolerate more types of intersections. Properties are explored, sample calculations are given, problems are raised (notably concerning dependence on stratification), and possible applications are mentioned.

MSC:

55N33 Intersection homology and cohomology in algebraic topology
57N80 Stratifications in topological manifolds

Citations:

Zbl 0448.55004
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