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: 10.5802/crmath.155
Classification: 57S05, 57M50, 57M60, 20F65, 22F05, 53C10, 57S25
Cornulier, Yves 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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Cornulier, Yves. Property FW and 1-dimensional piecewise groups. Comptes Rendus. Mathématique, Volume 359 (2021) no. 1, pp. 71-78. doi : 10.5802/crmath.155. http://www.numdam.org/articles/10.5802/crmath.155/

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