Intersection homology Kunneth theorems

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.