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 $${{\,\mathrm{F}\,}}_\infty $$ . The proof utilized certain contractible cube complexes, which in this paper prove $${{\,\mathrm{CAT}\,}}(0)$$ We then use fact to compute geometric invariants $$\Sigma ^m(F_{{\text {br}}})$$ pure group $$F_{{\text {br}}}$$ Only first invariant ^1(F_{{\text was previously known. A consequence our computation is as soon a subgroup containing commutator $$[F_{{\text {br}}},F_{{\text {br}}}]$$ finitely presented, it automatically