The chain-level intersection pairing for PL pseudomanifolds revisited
Geometric Topology
2018-12-31 v2 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.1609.05975,
title = {The chain-level intersection pairing for PL pseudomanifolds revisited},
author = {Greg Friedman},
journal= {arXiv preprint arXiv:1609.05975},
year = {2018}
}
Comments
47 pages; several updates including rewrite of introduction