A finitely-generated amenable group with very poor compression into Lebesgue spaces
Metric Geometry
2019-12-19 v2 Group Theory
Abstract
We construct an example of a finitely-generated amenable group that does not admit any coarse 1-Lipschitz embedding with positive compression exponent into L_p for any 1 \leq p < \infty, answering positively a question of Arzhantseva, Guba and Sapir.
Keywords
Cite
@article{arxiv.0909.2047,
title = {A finitely-generated amenable group with very poor compression into Lebesgue spaces},
author = {Tim Austin},
journal= {arXiv preprint arXiv:0909.2047},
year = {2019}
}
Comments
36 pages; [TDA, April 5th 2011:] modified slightly following referee reports