English

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

R2 v1 2026-06-21T13:45:07.614Z