  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.
