Dehn filling and Einstein metrics in higher dimensions

TL;DR

This paper extends Thurston's Dehn surgery theory to higher-dimensional Einstein metrics, providing a method to generate numerous new Einstein metrics on compact manifolds.

Contribution

It generalizes Dehn filling concepts from 3-manifolds to higher dimensions, creating a framework for constructing many new Einstein metrics.

Findings

Established a higher-dimensional analogue of Dehn surgery for Einstein metrics

Generated large families of Einstein metrics on compact manifolds

Demonstrated the applicability of Thurston's theory beyond 3-manifolds

Abstract

We prove that many features of Thurston's Dehn surgery theory for hyperbolic 3-manifolds generalize to Einstein metrics in any dimension. In particular, this gives large, infinite families of new Einstein metrics on compact manifolds.