De Matt Durham
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 the sublinear-Morse boundary to more broadly capture these generic directions.
In joint work with Abdul Zalloum, we develop the geometric foundations of sublinear-Morseness in the mapping class group and Teichmuller space. We prove that their sublinearly-Morse boundaries are visibility spaces and admit continuous equivariant injections into the boundary of the curve graph. Moreover, we completely characterize sublinear-Morseness in terms of the hierarchical structure on these spaces.
Our techniques include developing tools for modeling sublinearly-Morse rays via CAT(0) cube complexes. Part of this analysis involves establishing a direct connection between the geometry of the curve graph and the combinatorics of hyperplanes in these cubical models.
De Koji Fujiwara
De Emily Stark
De Kathryn Mann
De Pallavi Dani
De Carolyn Abbott
De Alice Kerr
De Jean Lecureux
De Nir Lazarovich
De Sam Shepherd
De Alessandro Sisto
De Stephen Coombes , Peter Liddle
De Ariane Trescases
De Albert Schwarz
De François-Xavier Vialard
De Thibaut Le Gouic
De Elsa Cazelles
