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

2024/03/25 by Fernós, Talia
#05E18 #06A07 #20E05 #20F29 #60B05 #FOS: Mathematics #Group Theory (math.GR) #Primary 20F65 #Secondary 05C12

paper · doi:10.48550/arxiv.2403.16360

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 2^N, where N is bounded by the dimension. This is a slight extension of the author's previous Tits' Alternative.

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