The moduli space of nonnegatively curved metrics on quotients of S2 × S3 by involutions

Abstract

We show that for an orientable non-spin manifold with fundamental group Z2 and universal cover S2×S3, the moduli space of metrics of nonnegative sectional curvature has infinitely many path components. The representatives of the components are quotients of the standard metric on S3×S3 or metrics on Brieskorn varieties previously constructed using cohomogeneity one actions. The components are distinguished using the relative η invariant of the spinc Dirac operator computed by means of a Lefschetz fixed point theorem.