CONNECTIVITY AT INFINITY FOR STATE SPACES OF COMPLETE BIPARTITE GRAPHS

The state or configuration space for r vertices on a complete bipartite graph K-m,K-n is a CAT(0) cube complex, which is sometimes interpreted as a parameter space for r robots moving on a K-m,K-n. 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 the universal covers of these complexes are connected at infinity.