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

McFeely Jackson Goodman; Jonathan Wermelinger

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arXiv · 2204.01189

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

McFeely Jackson Goodman·Jonathan Wermelinger

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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.

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BibTeX RIS

McFeely Jackson Goodman, Jonathan Wermelinger. 2022-04-04. The moduli Space of nonnegatively curved metrics on quotients of $S^2\times S^3$ by involutions. https://arxiv.org/abs/2204.01189

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