The chain-level intersection pairing for PL pseudomanifolds revisited

Greg Friedman

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arXiv · 1609.05975

The chain-level intersection pairing for PL pseudomanifolds revisited

Greg Friedman

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Abstract

We generalize the PL intersection product for chains on PL manifolds and for intersection chains on PL stratified pseudomanifolds to products of locally finite chains on non-compact spaces that are natural with respect to restriction to open sets. This is necessary to sheafify the intersection product, an essential step in proving duality between the Goresky-MacPherson intersection homology product and the intersection cohomology cup product pairing recently defined by the author and McClure. We also provide a correction to the Goresky-MacPherson proof of a version of Poincar\'e duality on pseudomanifolds that is used in the construction of the intersection product.

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Greg Friedman. 2016-09-20. The chain-level intersection pairing for PL pseudomanifolds revisited. https://arxiv.org/abs/1609.05975

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