English

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

R2 v1 2026-06-22T15:54:50.695Z