Ideal boundary of 7-systolic complexes and groups

TL;DR

This paper investigates the properties of boundaries of 7-systolic groups, proving strong asphericity and connectivity features that inform their potential splittings and topological structure.

Contribution

It establishes the strong hereditary asphericity of the ideal boundary of 7-systolic groups and analyzes boundary connectivity and cut points for certain classes.

Findings

Ideal boundary of 7-systolic groups is strongly hereditarily aspherical.

Some 7-systolic groups have connected boundaries without local cut points.

Results provide insights into group splittings based on boundary topology.

Abstract

We prove that ideal boundary of a 7-systolic group is strongly hereditarily aspherical. For some class of 7-systolic groups we show their boundaries are connected and without local cut points, thus getting some results concerning splittings of those groups.