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Intersection homology
duality and pairings: singular, PL and sheaf-theoretic
Greg Friedman and James E McClure |
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Algebraic & Geometric Topology 21 (2021) 3221–3301
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Abstract |
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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. |
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Keywords
intersection homology, intersection cohomology,
pseudomanifold, cup product, cap product, intersection
product, Poincaré duality, Verdier duality, sheaf theory
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Mathematical Subject Classification 2010
Primary: 55N33, 55N45
Secondary: 55N30, 57Q99
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References |
Publication
Received: 5 February 2019
Revised: 15 June 2020
Accepted: 10 July 2020
Published: 28 December 2021
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Authors |
| Greg Friedman | |
| Department of Mathematics Texas Christian University Fort Worth, TX United States |
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| James E McClure | |
| Department of Mathematics Purdue University West Lafayette, IN United States |
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