Characterizing stable subgroups
Tarik Aougab (Brown)
Abstract: A finitely generated subgroup H of a group G is said to be stable
in G if it satisfies a certain strong version of quasiconvexity, which
turns out to be a natural generalization of the notion of "convex
cocompact" for Kleinian groups and for subgroups of the mapping class
group. We give new characterizations of stability, and we use them to find
stable subgroups of the outer automorphism group of the free group and of
relatively hyperbolic groups. This relies on new ways of recognizing the
property of "Morse stability" for a geodesic g, which essentially states
that quasi-geodesics with end points on g lie Hausdorff close to g, in an
arbitrary metric space. Joint with Matthew Durham and Samuel Taylor.