# On the fundamental group of complete manifolds with almost Euclidean volume growth

## TL;DR

This paper proves that complete Riemannian manifolds with nonnegative Ricci curvature and specific volume growth conditions have trivial or finite fundamental groups, advancing understanding of their topological structure.

## Contribution

It establishes new results linking volume growth conditions to the finiteness or triviality of the fundamental group in manifolds with nonnegative Ricci curvature.

## Key findings

- Fundamental group is trivial under certain conditions.
- Fundamental group is finite with specific volume growth.
- Provides new insights into topology of manifolds with nonnegative Ricci curvature.

## Abstract

It is proved that the fundamental group of a complete Riemannian manifold with nonnegative Ricci curvature and certain volume growth conditions is trivial or finite.