A gap property for the growth of closed 3-manifold groups

TL;DR

This paper establishes a lower bound for the exponential growth rate of fundamental groups of closed nonflat nonpositively curved 3-manifolds and explores their growth properties in detail.

Contribution

It introduces a new lower bound for the uniform exponential growth rate and provides an in-depth analysis of growth behavior in these 3-manifold groups.

Findings

Lower bound for exponential growth rate established

Detailed analysis of growth properties of 3-manifold groups

Insights into the structure of nonpositively curved 3-manifold groups

Abstract

We provide a lower bound for the uniform exponential growth rate of closed nonflat nonpositively curved 3-manifold groups. A detailed study of the uniform exponential growth rate of closed 3-manifold groups is also presented.