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Intersection cohomology of cs-spaces and Zeeman’s filtration. (English) Zbl 0759.55003

This paper generalizes the notion of intersection homology in a number of ways. In particular, it extends the sheaf-theoretic definition of intersection homology to a more natural collection of stratified sets (cs-spaces) and allows more general perversities. These perversities are interesting in that they integrate more information from the singular part of the stratified set. For an ordinary perversity, the intersection cohomology sheaves are determined by their restriction to a submanifold with codimension \(\geq 2\). The generalized perversities are determined by a perhaps singular open subset whose complement has greater codimension. As an application, the authors extend McCrory’s results on Zeeman’s homology filtration to cs-spaces and show that it is the same as the filtration induced by a certain sequence of their generalized perversities.

MSC:

55N33 Intersection homology and cohomology in algebraic topology
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