Compression bounds for wreath products
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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.References
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Additional Information
- Sean Li
- Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012-1185
- MR Author ID: 899540
- Email: seanli@cims.nyu.edu
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2701-2714
- MSC (2010): Primary 20F65, 51F99
- DOI: https://doi.org/10.1090/S0002-9939-10-10307-4
- MathSciNet review: 2644886