Sublinearly Morse boundaries from the viewpoint of combinatorics

Merlin Incerti-Medici; Abdul Zalloum

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arXiv · 2101.01037

Sublinearly Morse boundaries from the viewpoint of combinatorics

Merlin Incerti-Medici·Abdul Zalloum

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Abstract

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(0) cube complexes, convergence to sublinearly Morse geodesic rays has a simple combinatorial description using the hyperplanes crossed by such sequences. As an application of this combinatorial description, we show that a certain subspace of the Roller boundary continously surjects on the subspace of the visual boundary consisting of sublinearly Morse geodesic rays.

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Merlin Incerti-Medici, Abdul Zalloum. 2021-01-04. Sublinearly Morse boundaries from the viewpoint of combinatorics. https://arxiv.org/abs/2101.01037

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