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Proper actions of wreath products and generalizations


Authors: Yves Cornulier, Yves Stalder and Alain Valette
Journal: Trans. Amer. Math. Soc. 364 (2012), 3159-3184
MSC (2010): Primary 20F69; Secondary 20E22, 43A05, 43A65
DOI: https://doi.org/10.1090/S0002-9947-2012-05475-4
Published electronically: February 9, 2012
MathSciNet review: 2888241
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Abstract: We study stability properties of the Haagerup Property and of coarse embeddability in a Hilbert space, under certain semidirect products. In particular, we prove that they are stable under taking standard wreath products. Our construction also provides a characterization of subsets with relative Property T in a standard wreath product.


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Additional Information

Yves Cornulier
Affiliation: Laboratoire de Mathématiques, Bâtiment 425, Université Paris-Sud, 91405 Orsay, France
Email: yves.cornulier@math.u-psud.fr

Yves Stalder
Affiliation: Laboratoire de Mathématiques, UMR 6620-CNRS, Université Blaise Pascal, Campus des Cézeaux, BP 80026, 63171 Aubière Cedex France
Email: yves.stalder@math.univ-bpclermont.fr

Alain Valette
Affiliation: Institut de Mathématiques, Université de Neuchâtel, Rue Émile Argand 11, CP 158, 2009 Neuchâtel, Switzerland
Email: Alain.Valette@unine.ch

DOI: https://doi.org/10.1090/S0002-9947-2012-05475-4
Keywords: Wreath product, measured walls, Haagerup Property, coarse embedding, Kazhdan’s Property T
Received by editor(s): December 8, 2009
Received by editor(s) in revised form: September 14, 2010
Published electronically: February 9, 2012
Additional Notes: The first and second authors were supported by ANR project “QuantiT” (Nr JC08_318197).
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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