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Abstract
Abstract We prove that the sublinearly Morse boundary of CAT ( 0 ) {\mathrm{CAT}(0)} cubulated groups with factor systems continuously injects in the Gromov boundary of a certain hyperbolic graph Γ. We also show that for all CAT ( 0 ) {\mathrm{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 continuously surjects on the subspace of the visual boundary consisting of sublinearly Morse geodesic rays.
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