Structure of fundamental groups of manifolds with Ricci curvature bounded below

TL;DR

This paper proves a generalized Margulis Lemma for manifolds with lower Ricci curvature bounds, leading to finiteness results for their fundamental groups under certain geometric constraints.

Contribution

It establishes a new generalized Margulis Lemma for Ricci-bounded manifolds, extending Gromov's conjecture and deriving finiteness results for fundamental groups.

Findings

Proved a generalized Margulis Lemma for Ricci curvature bounded below.

Derived finiteness results for fundamental groups of compact manifolds.

Applied results to manifolds with bounded diameter and Ricci curvature.

Abstract

Verifying a conjecture of Gromov we establish a generalized Margulis Lemma for manifolds with lower Ricci curvature bound. Among the various applications are finiteness results for fundamental groups of compact $n$-manifolds with upper diameter and lower Ricci curvature bound modulo nilpotent normal subgroups.