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.
Highlights
We prove that the group of piecewise homographic self-transformations of the real projective line, has “few” infinite subgroups with Property FW
We provide a complete proof, whose main tools are the use of the notion of partial action and of one-dimensional geometric structures. 2020 Mathematics Subject Classification. 57S05, 57M50, 57M60, 20F65, 22F05, 53C10, 57S25
The purpose of this note is to extract from the long paper [9] a strong restriction on groups of piecewise homographic self-transformations of the real projective line
Summary
The purpose of this note is to extract from the long paper [9] a strong restriction on groups of piecewise homographic self-transformations of the real projective line. We start with introducing this group, and the rigidity properties we deal with, namely Kazhdan’s Property T and Property FW
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