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Published online by Cambridge University Press: 18 September 2020
We show that oriented pseudomanifolds possess fundamental intersection homology classes, and we prove that intersection homology possesses a Poincaré duality given by the cap product with the fundamental class. We also prove Lefschetz duality for pseudomanifolds with boundary. We derive from both of these dualities nonsingular cup product and torsion pairings. We include an expositional survey of intersection pairings and the original approach of Goresky and MacPherson to intersection homology duality using such pairings.
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