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

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 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 if the dimension of is at least 5 and is not simply-connected.
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