31 citations · 62 across the 20 of their papers we have counts for
7 papers · 1 filter
Largest hyperbolic actions of 3--manifold groups
Carolyn Abbott, Hoang Thanh Nguyen, Alexander J. Rasmussen
The set of equivalence classes of cobounded actions of a group G on different hyperbolic metric spaces carries a natural partial order. Following Abbott--Balasubramanya--Osin, the…
Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups
Carolyn Abbott, Mark Hagen, Harry Petyt +1
We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic gr…
Hyperbolic projections and topological invariance of sublinearly Morse boundaries
Carolyn Abbott, Merlin Incerti-Medici
We show that the sublinearly Morse boundary of a CAT(0) cubical group with a factor system is well-defined up to homeomorphism with respect to the visual topology. The key tool use…
Shifts maps are not type-preserving
Carolyn Abbott, Nicholas Miller, Priyam Patel
For a surface of sufficient complexity, Dehn twists act elliptically on the arc, curve, and relative arc graph of . We show that composing a Dehn twist with a shift map resu…
Infinite-type loxodromic isometries of the relative arc graph
Carolyn R. Abbott, Nicholas Miller, Priyam Patel
An infinite-type surface is of type if it has an isolated puncture and admits shift maps. This includes all infinite-type surfaces with an isolated puncture o…
A new construction of subgroups of big mapping class groups
Carolyn R. Abbott, Hannah Hoganson, Marissa Loving +2
We explicitly construct new subgroups of the mapping class groups of an uncountable collection of infinite-type surfaces, including, but not limited to, free groups, Baumslag-Solit…
Random walks and quasi-convexity in acylindrically hyperbolic groups
C. Abbott, M. Hull
It is known that every infinite index quasi-convex subgroup of a non-elementary hyperbolic group is a free factor in a larger quasi-convex subgroup of . We give a probab…