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Irreducible lattices, invariant means, and commensurating actions

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We study rigidity properties of lattices in terms of invariant means and commensurating actions (or actions on CAT(0) cube complexes). We notably study Property FM for groups, namely that any action on a discrete set with an invariant mean has a finite orbit.

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Acknowledgments

I thank Bachir Bekka for discussions and pointing out [4]; I also thank Alain Valette for some useful references. I am grateful to the referee for pointing out many inaccuracies and for valuable suggestions.

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  1. Laboratoire de Mathématiques, Bâtiment 425, Université Paris-Sud 11, 91405 , Orsay, France

    Yves Cornulier

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  1. Yves Cornulier
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Correspondence to Yves Cornulier.

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Supported by ANR Grant GSG 12-BS01-0003-01.

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Cornulier, Y. Irreducible lattices, invariant means, and commensurating actions. Math. Z. 279, 1–26 (2015). https://doi.org/10.1007/s00209-014-1355-x

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  • DOI: https://doi.org/10.1007/s00209-014-1355-x

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