Moduli space of metrics of nonnegative sectional or positive Ricci curvature on Brieskorn quotients in dimension 5

TL;DR

This paper proves that the moduli spaces of nonnegative sectional and positive Ricci curvature metrics on certain 5-dimensional Brieskorn quotient manifolds have infinitely many disconnected components.

Contribution

It establishes the existence of infinitely many path components in the moduli spaces of these curvature metrics on specific 5-dimensional manifolds.

Findings

Moduli space of nonnegative sectional curvature metrics has infinitely many components.

Moduli space of positive Ricci curvature metrics also has infinitely many components.

Abstract

We show that the moduli space of Riemannian metrics of nonnegative sectional curvature on certain quotients of Brieskorn varieties in dimension 5 has infinitely many path components. The same is true for the corresponding moduli space of positive Ricci curvature.