Intersection homology Kunneth theorems

TL;DR

This paper extends the intersection homology Kunneth theorem to biperversities, broadening its applicability and recovering previous results under more general conditions.

Contribution

It generalizes the intersection homology Kunneth theorem to biperversities, relaxing conditions and unifying previous results.

Findings

Established a Kunneth theorem for biperversities in intersection homology.

Proved the theorem holds under relaxed biperversity conditions.

Recovered Cohen-Goresky-Ji Kunneth theorem as a special case.

Abstract

Cohen, Goresky and Ji showed that there is a Kunneth theorem relating the intersection homology groups $I^{\bar p}H_*(X\times Y)$ to $I^{\bar p}H_*(X)$ and $I^{\bar p}H_*(Y)$, provided that the perversity $\bar p$ satisfies rather strict conditions. We consider biperversities and prove that there is a K\"unneth theorem relating $I^{\bar p,\bar q}H_*(X\times Y)$ to $I^{\bar p}H_*(X)$ and $I^{\bar q}H_*(Y)$ for all choices of $\bar p$ and $\bar q$. Furthermore, we prove that the Kunneth theorem still holds when the biperversity $p,q$ is "loosened" a little, and using this we recover the Kunneth theorem of Cohen-Goresky-Ji.