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

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.

14 pages, 2 figures. Accepted for publication in Mathematische Zeitschrift. Video abstract available here: https://www.youtube.com/watch?v=ew3is8UTw6k

References in corpus (3)

• Boundary conditions for scalar curvature
• Moduli space of nonnegatively curved metrics on manifolds of dimension $4k+1$
• Bundles with non-multiplicative $\hat{A}$-genus and spaces of metrics with lower curvature bounds