8 citations · 11 across the 16 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…