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Comptes Rendus. Mathématique
Group theory
Property FW and 1-dimensional piecewise groups
Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 71-78.

Property FW is a natural combinatorial weakening of Kazhdan’s Property T. We prove that the group of piecewise homographic self-transformations of the real projective line, has “few” infinite subgroups with Property FW. In particular, no such subgroup is amenable or has Kazhdan’s Property T. These results are extracted from a longer paper. We provide a complete proof, whose main tools are the use of the notion of partial action and of one-dimensional geometric structures.

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DOI: https://doi.org/10.5802/crmath.155
Classification: 57S05,  57M50,  57M60,  20F65,  22F05,  53C10,  57S25
Yves Cornulier 1

1. CNRS and Univ Lyon, Univ Claude Bernard Lyon 1, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, 69622 Villeurbanne, France.
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Yves Cornulier. Property FW and 1-dimensional piecewise groups. Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 71-78. doi : 10.5802/crmath.155. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.155/

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