Intersection homology Kunneth theorems

摘要

Cohen, Goresky, and Ji showed that there is a Kunneth theorem relating the intersection homology groups Ip-barH_*(X×Y) to Ip-baeH_*(X) and Ip-barH_*(Y),provided that the perversity p-bar satisfies rather strict conditions.We consider biperversities and prove that there is a Kunneth theorem relating Ip-bar, q-bar H_*(X × Y ) to Ip-barH_*(X) and Iq-barH_*(Y)for all choices of p-bar and q-bar. Furthermore, we prove that the Kunneth theorem still holds when the biperversity p, q is “loosened” a little, and using this we recover theKunneth theorem of Cohen–Goresky–Ji.