Intersection homology Künneth theorems

Cohen, Goresky and Ji showed that there is a Künneth theorem relating the intersection homology groups I H∗(X × Y ) to I H∗(X) and I H∗(Y ), provided that the perversity p̄ satisfies rather strict conditions. We consider biperversities and prove that there is a Künneth theorem relating I H∗(X × Y ) to I H∗(X) and I H∗(Y ) for all choices of p̄ and q̄. Furthermore, we prove that the Künneth theorem still holds when the biperversity p, q is “loosened” a little, and using this we recover the Künneth theorem of Cohen-Goresky-Ji.