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We show that a finitely generated subgroup of the genus two handlebody group is stable if
and only if the orbit map to the disk graph is a quasi-isometric embedding. To this end, we …

The ray graph is a Gromov-hyperbolic graph on which the mapping class group of the plane
minus a Cantor set acts by isometries. We give a description of the Gromov boundary of the …

We show that a finitely generated subgroup of the genus 2 handlebody group is stable if and
only if the orbit map to the disk graph is a quasi-isometric embedding. To this end, we prove …

We study two actions of big mapping class groups. The first is an action by isometries on a
Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which …

Let S be an orientable surface of finite type. Using Pho-on's infinite unicorn paths, we prove
the hyperfiniteness of orbit equivalence relations induced by the actions of the mapping …

Let $\Sigma $ be a compact, orientable surface, and let $\Gamma $ be a relation on its
boundary components such that the prescribed arc graph $\mathcal {A}(\Sigma,\Gamma) …

We prove that the saddle connection graph associated to any half-translation surface is $4 $–
hyperbolic and uniformly quasi-isometric to the regular countably infinite-valent tree …

Two simultaneous actions of big mapping class groups Page 1 TRANSACTIONS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 376, Number 11, November 2023, Pages …

In the setting of hyperbolic groups, quasiconvex subgroups are particularly wellbehaved
subgroups. Specifically, quasiconvex subgroups of hyperbolic groups are precisely the …