Boundaries of systolic groups

TL;DR

This paper constructs EZ-structure boundaries for systolic groups, leading to the proof of the Novikov conjecture for torsion-free cases, by analyzing geodesic-like structures in systolic complexes.

Contribution

It introduces a novel boundary construction for systolic groups that parallels CAT(0) geodesics, enabling new topological and conjectural results.

Findings

Boundaries are EZ-structures for all systolic groups

Proves the Novikov conjecture for torsion-free systolic groups

Establishes properties of systolic geodesics similar to CAT(0) spaces

Abstract

For all systolic groups we construct boundaries which are EZ--structures. This implies the Novikov conjecture for torsion--free systolic groups. The boundary is constructed via a system of distinguished geodesics in a systolic complex, which we prove to have coarsely similar properties to geodesics in CAT(0) spaces.