Closed BLD-elliptic manifolds have virtually Abelian fundamental groups

TL;DR

This paper proves that closed, oriented Riemannian manifolds admitting a bounded length distortion branched cover from Euclidean space have fundamental groups that are virtually Abelian, linking geometric properties to algebraic group structure.

Contribution

It establishes a new connection between geometric covering properties and the algebraic structure of fundamental groups in Riemannian geometry.

Findings

Manifolds with bounded length distortion branched covers have virtually Abelian fundamental groups.

The result applies to closed, oriented Riemannian manifolds.

Provides a geometric criterion for algebraic properties of fundamental groups.

Abstract

We show that a closed, connected, oriented, Riemannian $n$-manifold, admitting a branched cover of bounded length distortion from $\mathbb R^n$, has a virtually Abelian fundamental group.