Geometric structures related to the braided Thompson groups

In previous work, joint with Bux, Fluch, Marschler and Witzel, we proved that the braided Thompson groups are of type F-infinity. The proof utilized certain contractible cube complexes, which in this paper we prove are CAT(0). We then use this fact to compute the geometric invariants Sigma(m)( F-br) of the pure braided Thompson group F-br. Only the first invariant Sigma(1)(F-br) was previously known. A consequence of our computation is that as soon as a subgroup of F-br containing the commutator subgroup [F-br, F-br] is finitely presented, it is automatically of type F-infinity.