Finiteness properties of the braided Thompson group

J. Meier

Thompson’s group V is often described as the group of dyadic homeomorphisms of the Cantor set. An element of V is described by taking two rooted binary trees (describing two decompositions of the Cantor set) along with a permutation of the leaves of the trees (describing a permutation of the subCantor sets). Matt Brin has introduced a braided version of this group, where instead of simply permuting the subCantor sets, one braids them. In joint work with Matt Brin, I have shown that this braided Thompson group ”BV” has many nice homological properties. In particular, it is of type F_{∞}, meaning it has a classifying space with finitely many cells in each dimension.