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math.GT2022★ 1 cited
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…
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…
math.MG2022
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…