The moduli Space of nonnegatively curved metrics on quotients of $S^2\times S^3$ by involutions

Abstract

We show that for an orientable non-spin manifold with fundamental group ${\mathbb{Z}}_2$ and universal cover $S^2\times S^3,$ 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 $S^3\times S^3$ or metrics on Brieskorn varieties previously constructed using cohomogeneity one actions. The components are distinguished using the relative $\eta$ invariant of the spin${}^c$ Dirac operator computed by means of a Lefschetz fixed point theorem.

12 pages

Cited by in corpus (1)

• Moduli space of nonnegatively curved metrics on manifolds of dimension $4k+1$