Stability in mapping class groups and right-angled Artin groups
Sam Taylor (Yale)
Abstract:
A well studied question in surface topology asks whether every purely
pseudo-Anosov subgroup of the mapping class group is convex cocompact. This
question can be reformulated in a way which references only the geometric
structure of the mapping class group using a strong form of quasiconvexity
called stability.
In joint work with Thomas Koberda and Johanna Mangahas, we recently gave a
complete characterization of stable subgroups of right-angled Artin groups
(RAAGs), thus answering the RAAG analog of the question above. In
particular, we show that any finitely generated subgroup of a RAAG all of
whose nontrivial elements have cyclic centralizer is stable and, in
particular, quasiconvex. In this talk, I will introduce the general notion
of stability, explain its importance in RAAGs, and give some applications of
our theorem.