Spaces of Positive Scalar Curvature metrics on totally nonspin Manifolds with spin boundary

DOI10.1007/S00209-023-03270-1zbMath1519.53033arXiv2204.11512WikidataQ122654893 ScholiaQ122654893MaRDI QIDQ6397376

Publication date: 25 April 2022

Abstract: In this article we study the space of positive scalar curvature metrics on totally nonspin manifolds with spin boundary. We prove that for such manifolds of certain dimensions, those spaces are not connected and have nontrivial fundamental group. Furthermore we show that a well-known propagation technique for detection results on spaces of positive scalar curvature metrics on spin manifolds ceases to work in the totally nonspin case.

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Spin and Spin({}^c) geometry (53C27) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Homotopy groups of special spaces (55Q52) Manifolds of metrics (especially Riemannian) (58D17)

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