Topology of open nonpositively curved manifolds

TL;DR

This survey reviews the topological properties of open, complete nonpositively curved manifolds, focusing on their ends, fundamental groups, and known examples, including cases with infinite volume.

Contribution

It compiles and discusses existing results on the topology of nonpositively curved manifolds, highlighting key properties and examples.

Findings

Topology of ends is well-understood in certain cases.

Restrictions on fundamental groups are significant in classifying these manifolds.

Known examples illustrate the diversity of topological structures.

Abstract

This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.