Connectivity at infinity for braid groups on complete graphs. (Q354253)

The authors find connectivity at infinity of braid groups of complete graphs. The main theorem of the paper states that the universal cover \(\widetilde{C_m(K_{m+n})}\) of the \(m\)-point discrete configuration space \(C_m(K_{m+n})\) of the complete graph \(K_{m+n}\) on \(n+m\) vertices is \((v_{m,n}-2)\)-connected at infinity but not \((v_{m,n}-1)\)-connected at infinity; here \(v_{m,n}=\min\bigl\{m,n,\bigl\lfloor\frac{m+n+1}{3}\bigr\rfloor\bigr\}\).