Property FW and 1-dimensional piecewise groups

Abstract

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.

10 pages. v2: expanded introduction

References in corpus (2)

• Commensurating actions for groups of piecewise continuous transformations
• Regularization of birational actions of FW groups

Cited by in corpus (1)

• Commensurating actions for groups of piecewise continuous transformations