Moduli spaces of nonnegative sectional curvature and non-unique souls

TL;DR

This paper investigates the structure of moduli spaces of nonnegative sectional curvature metrics on open manifolds, showing that nearby metrics have isotopic souls, thus revealing topological distinctions within these spaces.

Contribution

It introduces the concept that souls of close nonnegatively curved metrics are ambiently isotopic, providing a new geometric approach to distinguish components of the moduli space.

Findings

Connected components of moduli spaces are distinguished using topological methods.

Souls of nearby metrics are ambiently isotopic, linking geometry and topology.

New techniques help classify nonnegative curvature metrics on open manifolds.

Abstract

We apply various topological methods to distinguish connected components of moduli spaces of complete Riemannian metrics of nonnegative sectional curvature on open manifolds. The new geometric ingredient is that souls of nearby nonnegatively curved metrics are ambiently isotopic.