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Le Conte de la Mesure sur les Complexes Cubiques CAT(0) (2403.16360v1)

Published 25 Mar 2024 in math.GR

Abstract: We revisit the topic of probability measures on CAT(0) cube complexes and prove that an amenable group acting on a CAT(0) cube complex, regardless of dimension, necessarily preserves an interval in the Roller compactification. In the finite dimensional case, we prove that there must be an orbit of cardinality $2N$, where $N$ is bounded by the dimension. This is a slight extension of the author's previous Tits' Alternative.

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