Event № 554
A Kleinian group is convex cocompact if its orbit in hyperbolic 3-space is quasi-convex or, equivalently, that it acts cocompactly on the convex hull of its limit set in in hyperbolic 3-space.
Subgroup stability is a strong quasi-convexity condition in finitely generated groups which is intrinsic to the geometry of the ambient group and generalizes the classical quasi-convexity condition above. Importantly, it coincides with quasi-convexity in hyperbolic groups and the notion of convex cocompactness in mapping class groups which was developed by Farb-Mosher, Kent-Leininger, and Hamenstädt.
Using the Morse boundary, I will describe an equivalent characterization of subgroup stability which generalizes the above boundary characterization from Kleinian groups. Along the way I will discuss some known results about stable subgroups of various groups, including the mapping class group and right-angled Artin groups. The talk will include joint work with Matthew Gentry Durham and joint work with David Hume.