Free actions of free groups on countable structures and property (T)

David M. Evans, and Todor Tsankov. "Free actions of free groups on countable structures and property (T)." Fundamenta Mathematicae 232.1 (2016): 49-63. <http://eudml.org/doc/282791>.

@article{DavidM2016,
abstract = {We show that if G is a non-archimedean, Roelcke precompact Polish group, then G has Kazhdan's property (T). Moreover, if G has a smallest open subgroup of finite index, then G has a finite Kazhdan set. Examples of such G include automorphism groups of countable ω-categorical structures, that is, the closed, oligomorphic permutation groups on a countable set. The proof uses work of the second author on the unitary representations of such groups, together with a separation result for infinite permutation groups. The latter allows the construction of a non-abelian free subgroup of G acting freely in all infinite transitive permutation representations of G.},
author = {David M. Evans, Todor Tsankov},
journal = {Fundamenta Mathematicae},
keywords = {oligomorphic groups; property (T); omega-categoricity; unitary representations; Roelcke precompact},
language = {eng},
number = {1},
pages = {49-63},
title = {Free actions of free groups on countable structures and property (T)},
url = {http://eudml.org/doc/282791},
volume = {232},
year = {2016},
}

TY - JOUR
AU - David M. Evans
AU - Todor Tsankov
TI - Free actions of free groups on countable structures and property (T)
JO - Fundamenta Mathematicae
PY - 2016
VL - 232
IS - 1
SP - 49
EP - 63
AB - We show that if G is a non-archimedean, Roelcke precompact Polish group, then G has Kazhdan's property (T). Moreover, if G has a smallest open subgroup of finite index, then G has a finite Kazhdan set. Examples of such G include automorphism groups of countable ω-categorical structures, that is, the closed, oligomorphic permutation groups on a countable set. The proof uses work of the second author on the unitary representations of such groups, together with a separation result for infinite permutation groups. The latter allows the construction of a non-abelian free subgroup of G acting freely in all infinite transitive permutation representations of G.
LA - eng
KW - oligomorphic groups; property (T); omega-categoricity; unitary representations; Roelcke precompact
UR - http://eudml.org/doc/282791
ER -