Connectedness at infinity of systolic complexes and groups

TL;DR

This paper investigates the connectedness at infinity of systolic groups, highlighting their differences from certain manifold groups and exploring their semistability at infinity.

Contribution

It introduces new insights into the connectedness and semistability properties at infinity of systolic groups, distinguishing them from other classes of groups.

Findings

Systolic groups have unique connectedness at infinity properties.

Systolic groups differ from fundamental groups of high-dimensional Euclidean manifolds.

Some systolic groups exhibit semistability at infinity.

Abstract

By studying connectedness at infinity of systolic groups we distinguish them from some other classes of groups, in particular from the fundamental groups of manifolds covered by euclidean space of dimension at least three. We also study semistability at infinity for some systolic groups.