31 citations · 62 across the 20 of their papers we have counts for
24 papers
Relative hyperbolicity, thickness, and the hierarchically hyperbolic boundary
Carolyn Abbott, Jason Behrstock, Jacob Russell
We study the boundaries of relatively hyperbolic HHGs. Using the simplicial structure on the hierarchically hyperbolic boundary, we characterize both relative hyperbolicity and bei…
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…
Structure invariant properties of the hierarchically hyperbolic boundary
Carolyn Abbott, Jason Behrstock, Jacob Russell
We prove several topological and dynamical properties of the boundary of a hierarchically hyperbolic group are independent of the specific hierarchically hyperbolic structure. This…
Valuations, completions, and hyperbolic actions of metabelian groups
Carolyn R. Abbott, Sahana Balasubramanya, Sam Payne +1
Actions on hyperbolic metric spaces are an important tool for studying groups, and so it is natural, but difficult, to attempt to classify all such actions of a fixed group. In thi…
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…
Higher rank confining subsets and hyperbolic actions of solvable groups
Carolyn R. Abbott, Sahana Balasubramanya, Alexander J. Rasmussen
Recent papers of the authors have completely described the hyperbolic actions of several families of classically studied solvable groups. A key tool for these investigations is the…
Acylindrically hyperbolic groups and their quasi-isometrically embedded subgroups
Carolyn R. Abbott, Jason F. Manning
We abstract the notion of an A/QI triple from a number of examples in geometric group theory. Such a triple (G,X,H) consists of a group G acting on a Gromov hyperbolic space X, acy…
Largest hyperbolic actions and quasi-parabolic actions in groups
Carolyn R. Abbott, Alexander J. Rasmussen
The set of equivalence classes of cobounded actions of a group on different hyperbolic metric spaces carries a natural partial order. The resulting poset thus gives rise to a notio…
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…
Hierarchically hyperbolic groups and uniform exponential growth
Carolyn Abbott, Thomas Ng, Davide Spriano +2
We give several sufficient conditions for uniform exponential growth in the setting of virtually torsion-free hierarchically hyperbolic groups. For example, any hierarchically hype…
Boundaries of coned-off hyperbolic spaces
Carolyn R. Abbott, Jason F. Manning
Coning off a collection of uniformly quasiconvex subsets of a Gromov hyperbolic space leaves a new space, called the cone-off. Kapovich and Rafi generalized work of Bowditch to sho…
Actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces
Carolyn R. Abbott, Alexander J. Rasmussen
We give a complete list of the cobounded actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces up to a natural equivalence relation. The set of equivalence classe…
Conjugator lengths in hierarchically hyperbolic groups
Carolyn Abbott, Jason Behrstock
In this paper, we establish upper bounds on the length of the shortest conjugator between pairs of infinite order elements in a wide class of groups. We obtain a general result whi…
Actions of small cancellation groups on hyperbolic spaces
Carolyn Abbott, David Hume
We generalize Gruber--Sisto's construction of the coned--off graph of a small cancellation group to build a partially ordered set of cobounded actions of a given sma…
The geometry of generalized loxodromic elements
Carolyn R. Abbott, David Hume
We explore geometric conditions which ensure a given element of a finitely generated group is, or fails to be, generalized loxodromic; as part of this we prove a generalization of…
Hyperbolic structures on groups
Carolyn Abbott, Sahana Balasubramanya, Denis Osin
For every group , we introduce the set of hyperbolic structures on , denoted , which consists of equivalence classes of (possibly infinite) generating sets of…
Largest acylindrical actions and stability in hierarchically hyperbolic groups
Carolyn Abbott, Jason Behrstock, Daniel Berlyne +2
We consider two manifestations of non-positive curvature: acylindrical actions on hyperbolic spaces and quasigeodesic stability. We study these properties for the class of hierarch…
Extending group actions on metric spaces
C. Abbott, D. Hume, D. Osin
We address the following natural extension problem for group actions: Given a group , a subgroup , and an action of on a metric space, when is it possible to extend…
Property for acylindrically hyperbolic groups
Carolyn R. Abbott, François Dahmani
We prove that every acylindrically hyperbolic group that has no non-trivial finite normal subgroup satisfies a strong ping pong property, the property: for any finite c…
Not all finitely generated groups have universal acylindrical actions
Carolyn R. Abbott
The class of acylindrically hyperbolic groups, which are groups that admit a certain type of non-elementary action on a hyperbolic space, contains many interesting groups such as n…