Singular chain intersection homology for traditional and super-perversities

Details Singular chain intersection homology for traditional and super-perversities Singular chain intersection homology for traditional and super-perversities

2004-07-16

arxiv.org/abs/math/0407301v1

Transactions of the American Mathematical Society 359 (2007), 1977-2019

Mathematics

Geometric Topology

46 pages; see also http://www.math.yale.edu/~friedman/superp3a.pdf

Scientific paper

We introduce a singular chain intersection homology theory which generalizes that of King and which agrees with the Deligne sheaf intersection homology of Goresky and MacPherson on any topological stratified pseudomanifold, compact or not, with constant or local coefficients, and with traditional perversities or superperversities (those satisfying p(2)>0). For the case p(2)=1, these latter perversitie were introduced by Cappell and Shaneson and play a key role in their superduality theorem for embeddings. We further describe the sheafification of this singular chain complex and its adaptability to broader classes of stratified spaces.

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