Intersection homology Künneth theorems (Q1000585)

The author studies the Künnneth property for intersection homology. The intersection homology does not possess a Künneth theorem in complete generality. The problem can be formulated as follows. Consider the \(PL\) pseudomanifolds \(X,Y\) and the perversities \(\tilde p, \tilde q\) and ask for the existence of a chain complex defined geometrically on \(X\times Y\) whose homology is isomorphic to that of \(I^{\tilde p} C_*(X)\otimes I^{\tilde q}C_*(Y)\). The author works in the setting of singular intersection homology on topological pseudomanifolds and shows that there are several choices of ``biperversities'' \(\tilde p,\tilde q\) associated to the product bifiltration of the product \(X\times Y\) in order to obtain a Künneth theorem. The main result is obtained in Theorem 3.2.