Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms

TL;DR

This paper investigates the structure of the space of positive scalar curvature metrics on topological spherical space forms, revealing the number of connected components for certain non-simply-connected cases in dimensions five and higher.

Contribution

It provides a classification of the path components of the metric and moduli space of positive scalar curvature metrics on topological spherical space forms, extending understanding in high-dimensional topology.

Findings

Determines the number of path components for non-simply-connected cases

Analyzes the moduli space structure of positive scalar curvature metrics

Focuses on manifolds of dimension at least 5

Abstract

Let $M$ be a topological spherical space form, i.e. a smooth manifold whose universal cover is a homotopy sphere. We determine the number of path components of the space and moduli space of Riemannian metrics with positive scalar curvature on $M$ if the dimension of $M$ is at least 5 and $M$ is not simply-connected.