Röver's simple group is of type f∞

We prove that Claas Röver's Thompson{Grigorchuk simple group V has type F1. The proof involves constructing two complexes on which V G acts a simplicial complex analogous to the Stein complex for V , and a polysimplicia complex analogous to the Farley complex for V . We then analyze the descendin links of the polysimplicial complex, using a theorem of Belk and Forrest to prov increasing connectivity.