Samuel J. Taylor

Convex cocompactness and stability in mapping class groups

We introduce a strong notion of quasiconvexity in finitely generated groups, which we call stability. Stability agrees with quasiconvexity in hyperbolic groups and is preserved under quasi-isometry for finitely generated groups. We show that the stable subgroups of mapping class groups are precisely the convex cocompact subgroups. This generalizes a well-known result of Behrstock and is related to questions asked by Farb and Mosher and by Farb. 20F65, 51H05; 57M07, 30F60

Hyperbolic extensions of free groups

Given a finitely generated subgroup

The co‐surface graph and the geometry of hyperbolic free group extensions

\Gamma \le \mathrm{Out}(\mathbb{F})

THE JONES POLYNOMIAL AND BOUNDARY SLOPES OF ALTERNATING KNOTS

of the outer automorphism group of the rank

A note on subfactor projections

r

Counting loxodromics for hyperbolic actions

free group

Pulling back stability with applications to Out(Fn) and relatively hyperbolic groups

\mathbb{F} = F_r

Convex cocompactness in mapping class groups via quasiconvexity in right-angled Artin groups

, there is a corresponding free group extension

Small intersection numbers in the curve graph

1 \to \mathbb{F} \to E_{\Gamma} \to \Gamma \to 1

Fibered faces, veering triangulations, and the arc complex

. We give sufficient conditions for when the extension