Free actions of free groups on countable structures and property (T)
File(s)
Accepted version
Author(s)
Evans, DM
Tsankov, T
Type
Journal Article
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.
Date Issued
2016-01-01
Date Acceptance
2016-01-01
Citation
Fundamenta Mathematicae, 2016, 232 (1), pp.49-63
ISSN
1730-6329
Publisher
Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics)
Start Page
49
End Page
63
Journal / Book Title
Fundamenta Mathematicae
Volume
232
Issue
1
Copyright Statement
This is a pre-print of the article: Free actions of free groups on countable structures and property (T). Volume 232 / 2016. David M. Evans, Todor Tsankov
Fundamenta Mathematicae 232(2016), 49-63. DOI: 10.4064/fm232-1-4
Fundamenta Mathematicae 232(2016), 49-63. DOI: 10.4064/fm232-1-4
Subjects
Science & Technology
Physical Sciences
Mathematics
oligomorphic groups
property (T)
omega-categoricity
unitary representations
Roelcke precompact
Publication Status
Published