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Isometries of CAT(0) cube complexes are semi-simple

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arxiv 0705.3386 v1 pith:2WEBFA76 submitted 2007-05-23 math.GR

Frédéric Haglund (LM-Orsay) This is my paper · ORCID
classification math.GR
keywords cubeactionadmitsarbitraryautomorphismaxiscombinatorialcomplex
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We show that an automorphism of an arbitrary CAT(0) cube complex either has a fixed point or preserves some combinatorial axis. It follows that when a group contains a distorted cyclic subgroup, it admits no proper action on a discrete space with walls.

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Cited by 1 Pith paper

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  1. On the Baum-Connes Conjecture for Groups Acting on CAT(0)-Cubical Spaces

    math.KT 2019-08 conditional novelty 6.0 of 10

    The authors construct a de Rham-type Kasparov cycle for groups acting on CAT(0)-cubical spaces and use it to reprove Baum-Connes with coefficients for these groups.

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