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

2022/04/04 by McFeely Jackson Goodman, Goodman, McFeely Jackson, Jonathan Wermelinger +1
Mathematics · Physics and Astronomy · #53C20 #53C27 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2204.01189

openalex publication_date 2022/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 spin^c Dirac operator computed by means of a Lefschetz fixed point theorem.

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