Equivariant spin bordism in low dimensions

Abstract

We study Ω Spin, Z p n , n=5, 6, 7, where p is an odd prime and we consider some applications to the existence of Z p -invariant metrics of positive scalar curvature on closed spin manifolds of dimensions 5, 6, 7. We show that for actions of “mixed type” the vanishing of the obstruction considered implies Z p -invariant positive scalar curvature.