Simplicial Volume of Closed Locally Homogeneous Riemannian Manifolds

TL;DR

This paper proves that closed, locally homogeneous Riemannian manifolds with positive simplicial volume are topologically equivalent to locally symmetric spaces of non-compact type.

Contribution

It establishes a topological classification linking positive simplicial volume to locally symmetric spaces in the context of locally homogeneous manifolds.

Findings

Positive simplicial volume implies the manifold is homeomorphic to a locally symmetric space of non-compact type.

Provides a classification criterion for locally homogeneous Riemannian manifolds based on simplicial volume.

Abstract

We show that every closed, locally homogeneous Riemannian manifold with positive simplicial volume must be homeomorphic to a locally symmetric space of non-compact type.