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Strong amenability and the infinite conjugacy class property

Frisch, Joshua and Tamuz, Omer and Vahidi Ferdowsi, Pooya (2019) Strong amenability and the infinite conjugacy class property. Inventiones Mathematicae, 218 (3). pp. 833-851. ISSN 0020-9910.

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A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite conjugacy class property.

Item Type:Article
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Tamuz, Omer0000-0002-0111-0418
Additional Information:© 2019 Springer-Verlag GmbH Germany, part of Springer Nature. Received: 16 March 2018; Accepted: 7 June 2019; Published online: 13 July 2019. This work was supported by a grant from the Simons Foundation (#419427, Omer Tamuz), and by NSF Grant DMS-1464475. We would like to thank Benjamin Weiss and Andrew Zucker for correcting mistakes in earlier drafts of this paper, and to likewise thank an anonymous referee for many corrections and suggestions. We would also like to thank Yair Hartman and Mehrdad Kalantar for drawing our attention to the relation of our results to the unique trace property of group von Neumann algebras.
Funding AgencyGrant Number
Simons Foundation419427
Issue or Number:3
Record Number:CaltechAUTHORS:20191114-102021413
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Official Citation:Frisch, J., Tamuz, O. & Vahidi Ferdowsi, P. Invent. math. (2019) 218: 833.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99832
Deposited By: Tony Diaz
Deposited On:14 Nov 2019 21:36
Last Modified:14 Nov 2019 21:36

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