Finitely-presented universal mapping class groups
Javier Aramayona (Madrid)
Monday 9th January, 2017 15:00-16:00 Maths 204
In this talk, we will define the "asymptotically rigid" mapping class group B_g of genus g. The group B_g is a subgroup of the mapping class group of a certain infinite-type surface, and contains the mapping class group of every compact surface of genus at most g with non-empty boundary.
The group B_g turns out to be finitely presented, and its k-th homology group coincides with the k-th stable homology of the mapping class group of genus g, for k small enough. In addition, the groups B_g so obtained behave very much like their finite-type counterparts; for instance, every automorphism is geometric, there are no (weakly) injective maps from B_g to B_h if g>h, and they admit no interesting homomorphisms from higher-rank lattices. In addition, B_g does not have Kazhdan's property (T) for any g.
This is joint work with Louis Funar (Grenoble)