Martin R. Bridson
Submitted October 2012. Accepted 11 March 2013. To appear in Math Res Lett
Abstract. There exist right angled Artin groups A such that the isomorphism
problem for finitely presented subgroups of A is unsolvable, and for certain
finitely presented subgroups the conjugacy and membership problems are unsolvable.
It follows that if S is a surface of finite type and the genus of S is sufficiently
large, then the corresponding decision problems for the mapping class group Mod(S) are unsolvable.
Every virtually special group embeds in the mapping class group of infinitely many
closed surfaces. Examples are given of nitely presented subgroups of mapping class
groups that have infinitely many conjugacy classes of torsion elements.
10 pages, no figures.