3 papers
math.GT2023
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…
math.GR2023
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…
math.GT2022
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…