Denis Sjerve - Genus actions on Riemann surfaces and spherical space forms

In this lecture we address the problem of which finite groups G admit effective analytic actions on some connected compact Riemann surface S so that all quotient surfaces S/H have genus , where H is any non-trivial subgroup of G. We relate this problem to the spherical space form problem through the associated action of G on the vector space V of holomorphic differentials on S.