Intersection homology Kunneth theorems

Abstract

Cohen, Goresky and Ji showed that there is a Kunneth theorem relating the intersection homology groups $I^{\bar{p}}{H}_{\ast }(X\times Y)$ to $I^{\bar{p}}{H}_{\ast }(X)$ and $I^{\bar{p}}{H}_{\ast }(Y)$, provided that the perversity $\bar{p}$ satisfies rather strict conditions. We consider biperversities and prove that there is a Künneth theorem relating $I^{\bar{p},\bar{q}}{H}_{\ast }(X\times Y)$ to $I^{\bar{p}}{H}_{\ast }(X)$ and $I^{\bar{q}}{H}_{\ast }(Y)$ 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.

26 pages

References in corpus (1)

• On the chain-level intersection pairing for PL manifolds