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

TL;DR

This paper investigates the topology of the space of positive scalar curvature metrics on totally nonspin manifolds with spin boundary, revealing non-connectedness and limitations of existing detection techniques.

Contribution

It demonstrates that these metric spaces are not connected and have nontrivial fundamental groups, and shows the failure of a key propagation technique in the nonspin setting.

Findings

Spaces are not connected and have nontrivial fundamental groups

Propagation techniques for detection fail in nonspin cases

Results depend on the dimension of the manifolds

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.