8 citations · 11 across the 16 of their papers we have counts for
16 papers
Pseudo-Anosov flows and the geometry of Anosov-like group actions
Thomas Barthelmé, Kathryn Mann, Neige Paulet +1
We show that the action on its orbit space induced by a pseudo-Anosov flow on a closed -manifold (and more general Anosov-like actions) can be seen as an isometric action on a G…
Stable cylinders and fine structures for hyperbolic groups and curve graphs
Harry Petyt, Davide Spriano, Abdul Zalloum
In 1995, Rips and Sela asked if torsionfree hyperbolic groups admit globally stable cylinders. We establish this property for all residually finite hyperbolic groups and curve grap…
Growth tightness and genericity for word metrics from injective spaces
Lihuang Ding, Dídac Martínez-Granado, Abdul Zalloum
Mapping class groups are known to admit geometric (proper, cobounded) actions on injective spaces. Starting with such an action, and relying only on geometric arguments, we show th…
Constructing metric spaces from systems of walls
Harry Petyt, Abdul Zalloum, Davide Spriano
We give a general procedure for constructing metric spaces from systems of partitions. This generalises and provides analogues of Sageev's construction of dual CAT(0) cube complexe…
Effective flipping, skewering and rank rigidity for cubulated groups with factor systems
Abdul Zalloum
Relying on work of Caprace and Sageev \cite{capracesageev:rank}, we provide an effective form of rank rigidity in the context of groups virtually acting freely cocompactly on a CAT…
Injectivity, cubical approximations and equivariant wall structures beyond CAT(0) cube complexes
Abdul Zalloum
This is an expository survey with two goals. 1) The primary goal is to discuss and highlight the impact of two recent influential ideas in geometric group theory. The first of whic…
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…
Morse subsets of injective spaces are strongly contracting
Alessandro Sisto, Abdul Zalloum
We show that a quasi-geodesic in an injective metric space is Morse if and only if it is strongly contracting. Since mapping class groups and, more generally, hierarchically hyperb…
The geometry of genericity in mapping class groups and Teichmüller spaces via CAT(0) cube complexes
Matthew Gentry Durham, Abdul Zalloum
Random walks on spaces with hyperbolic properties tend to sublinearly track geodesic rays which point in certain hyperbolic-like directions. Qing-Rafi-Tiozzo recently introduced th…
Hyperbolic models for CAT(0) spaces
Harry Petyt, Davide Spriano, Abdul Zalloum
We introduce two new tools for studying CAT(0) spaces: \emph{curtains}, versions of cubical hyperplanes; and the \emph{curtain model}, a counterpart of the curve graph. These tools…
Sublinearly Morse boundaries from the viewpoint of combinatorics
Merlin Incerti-Medici, Abdul Zalloum
We prove that the sublinearly Morse boundary of every known cubulated group continuously injects in the Gromov boundary of a certain hyperbolic graph. We also show that for all CAT…
Convergence of sublinearly contracting horospheres
Abdul Zalloum
In \cite{QR19}, Qing, Rafi and Tiozzo introduced the sublinearly contracting boundary for CAT(0) spaces. Every point of this boundary is uniquely represented by a sublinearly contr…
Sublinearly Morse Geodesics in CAT(0) Spaces: Lower Divergence and Hyperplane Characterization
Devin Murray, Yulan Qing, Abdul Zalloum
We introduce the notion of k-lower divergence for geodesic rays in CAT(0) spaces. Building on the work of Charney and Sultan we give various characterizations of k-contracting geod…
Regularity of Morse geodesics and growth of stable subgroups
Matthew Cordes, Jacob Russell, Davide Spriano +1
We prove that Morse local-to-global groups grow exponentially faster than their infinite index stable subgroups. This generalizes a result of Dahmani, Futer, and Wise in the contex…
Geometry and dynamics on sublinearly Morse boundaries of CAT(0) groups
Yulan Qing, Abdul Zalloum
Given a sublinear function , -Morse boundaries $\pka X$ of proper \CAT spaces are introduced by Qing, Rafi and Tiozzo. It is a topological space that consists of a large set…
Regular Languages for Contracting Geodesics
Joshua Eike, Abdul Zalloum
Let be a finitely generated group. We show that for any finite generating set , the language consisting of all geodesics in with a contracting property is a regul…