A finitely-generated amenable group with very poor compression into Lebesgue spaces

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.

36 pages; [TDA, April 5th 2011:] modified slightly following referee reports

References in corpus (1)

• $L_p$ compression, traveling salesmen, and stable walks

Cited by in corpus (4)

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