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

Friedman, Greg; McClure, James E

doi:10.2140/agt.2021.21.3221

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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

DOI: 10.2140/agt.2021.21.3221

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

Volume 21, issue 7 (2021)