# On ends of finite-volume noncompact manifolds of nonpositive curvature

## TL;DR

This paper proves that for certain finite-volume noncompact manifolds with nonpositive curvature, the fundamental groups of their ends are almost nilpotent, confirming a longstanding folklore conjecture.

## Contribution

It establishes a conjecture linking the geometry of the universal cover to the algebraic structure of end fundamental groups in nonpositive curvature manifolds.

## Key findings

- Ends of the manifold have almost nilpotent fundamental groups.
- Universal cover being a visibility manifold implies algebraic properties of ends.
- Confirms a folklore conjecture in geometric topology.

## Abstract

In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold $M$ of finite volume with sectional curvature $-1 \leq K \leq 0$, if the universal cover of $M$ is a visibility manifold, then the fundamental group of each end of $M$ is almost nilpotent.