and Mapping Class Groups.

**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.