Asymptotic dimensions of mapping class groups and relatively Seminar

We prove that mapping class groups have finite Assouad-Nagata dimension
by showing they admit quasi-isometric embeddings into a finite product
of simplicial trees. For relatively hyperbolic groups, we show that they
have finite Assouad-Nagata dimension if and only if all peripheral
subgroups do. The method for achieving this is to prove a new
large-scale description of the quasi-trees of spaces axiomatised by
Bestvina-Bromberg-Fujiwara.