# Connectivity at Infinity for the Braid Group of a Complete Bipartite Graph

## TL;DR

This paper investigates the connectivity at infinity of the braid group on a complete bipartite graph, revealing detailed topological properties of the associated CAT(0) cube complex.

## Contribution

It provides an explicit computation of the connectivity at infinity for the graph braid group of a complete bipartite graph, combining topology, symmetry analysis, and existing results.

## Key findings

- Explicit degree of connectivity at infinity computed
- Topological links of vertices analyzed in detail
- Symmetries among parameters identified

## Abstract

The graph braid group of a complete bipartite graph is the fundamental group of a configuration space of points on the graph, which is a CAT(0) cube complex. We combine an analysis of the topology of links of vertices in this complex, the description of a hidden symmetry among the parameters, and known results from the literature to explicitly compute the exact degree to which these complexes and groups are connected at infinity.