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

Greg Friedman and James E McClure

Algebraic & Geometric Topology 21 (2021) 3221–3301
Abstract

We compare the sheaf-theoretic and singular chain versions of Poincaré 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.

Keywords
intersection homology, intersection cohomology, pseudomanifold, cup product, cap product, intersection product, Poincaré duality, Verdier duality, sheaf theory
Mathematical Subject Classification 2010
Primary: 55N33, 55N45
Secondary: 55N30, 57Q99
References
Publication
Received: 5 February 2019
Revised: 15 June 2020
Accepted: 10 July 2020
Published: 28 December 2021
Authors
Greg Friedman
Department of Mathematics
Texas Christian University
Fort Worth, TX
United States
James E McClure
Department of Mathematics
Purdue University
West Lafayette, IN
United States