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Compression bounds for wreath products

Author: Sean Li
Journal: Proc. Amer. Math. Soc. 138 (2010), 2701-2714
MSC (2010): Primary 20F65, 51F99
Published electronically: April 5, 2010
MathSciNet review: 2644886
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Abstract: We show that if $ G$ and $ H$ are finitely generated groups whose Hilbert compression exponent is positive, then so is the Hilbert compression exponent of the wreath product $ G \wr H$. We also prove an analogous result for coarse embeddings of wreath products. In the special case $ G=\mathbb{Z}$, $ H=\mathbb{Z} \wr \mathbb{Z}$ our result implies that the Hilbert compression exponent of $ \mathbb{Z}\wr (\mathbb{Z}\wr\mathbb{Z})$ is at least $ 1/4$, answering a question posed by several authors.

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Additional Information

Sean Li
Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012-1185

Received by editor(s): September 2, 2009
Received by editor(s) in revised form: December 3, 2009
Published electronically: April 5, 2010
Additional Notes: This work was supported in part by NSF grants CCF-0635078 and CCF-0832795.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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