Manifolds without conjugate points and their fundamental groups

TL;DR

This paper investigates the structure of fundamental groups of closed manifolds without conjugate points, showing that the centralizers of all elements virtually split, revealing new algebraic properties of these groups.

Contribution

It establishes that in such manifolds, the centralizers of all elements in the fundamental group virtually split, a novel structural insight.

Findings

Centralizers of all elements virtually split in these groups

Provides algebraic structure insights for manifolds without conjugate points

Advances understanding of fundamental groups in geometric topology

Abstract

We show that in the fundamental groups of closed manifolds without conjugate points centralizers of all elements virtually split.