Intersection homology duality and pairings: singular, PL, and sheaf-theoretic

Greg Friedman; James E. McClure

doi:10.2140/agt.2021.21.3221

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arXiv · 1812.10585

Intersection homology duality and pairings: singular, PL, and sheaf-theoretic

Greg Friedman·James E. McClure

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Abstract

We compare the sheaf-theoretic and singular chain versions of Poincare duality for intersection homology, showing that they are isomorphic via naturally defined maps. Similarly, we demonstrate the existence of canonical isomorphisms between the singular intersection cohomology cup product, the hypercohomology product induced by the Goresky-MacPherson sheaf pairing, and, for PL pseudomanifolds, the Goresky-MacPherson PL intersection product. We also show that the de Rham isomorphism of Brasselet, Hector, and Saralegi preserves product structures.

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Greg Friedman, James E. McClure. 2018-12-27. Intersection homology duality and pairings: singular, PL, and sheaf-theoretic. https://doi.org/10.2140/agt.2021.21.3221

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