The chain-level intersection product for PL pseudomanifolds revisited
Greg Friedman · Journal of Singularities · 2018
We revisit the construction of the PL intersection pairing for PL chains on PL manifolds and for PL intersection chains on PL stratied pseudomanifolds. We provide a correction to the Goresky-MacPherson proof of a version of Poincar e duality on pseudomanifolds that is necessary for the construction of the intersection pairing on pseudomanifolds, and we provide a construction of the intersection product for locally nite intersection chains on non-compact pseudomanifolds that reduces to the pre-existing (corrected) construction on compact pseudomanifolds. As an application of the techniques developed, we provide a direct proof that the Goresky-MacPherson homology intersection product is Poincar e dual to the cup product pairing on compact oriented PL manifolds, but we leave as an open question, with discussion of the diculties involved, whether an analogous proof can be formulated to demonstrate such a duality between intersection and cup product pairings for intersection homology of pseudomanifolds.