On the geometry of some Equivariantly related manifolds

TL;DR

This paper introduces a topological method to realize classical and exotic G-manifolds geometrically and applies Cheeger deformations to generate new metrics with positive Ricci and near non-negative curvature.

Contribution

It presents a novel topological procedure for geometric realization of G-manifolds and demonstrates its application in producing metrics with desirable curvature properties.

Findings

New metrics of positive Ricci curvature on G-manifolds

Almost non-negative curvature metrics constructed via Cheeger deformations

Topological realization of exotic manifolds

Abstract

We provide a topological procedure to obtain geometric realizations of both classical and `exotic' $G$-manifolds, such as spheres, bundles over spheres and Kervaire manifolds. As an application, we apply the process known as Cheeger deformations to produce new metrics of both positive Ricci and almost non-negative curvature on such objects.