Amenable groups with very poor compression into Lebesgue spaces

Tim Austin

Research output: Contribution to journalArticle

Abstract

We give a construction of finitely generated amenable groups that do not admit any coarse 1-Lipschitz embedding with positive compression exponent into L p for any 1 ≤ p < ∞, including some that are four-step solvable, answering positively a question posed by Arzhantseva, Guba, and Sapir.

Original languageEnglish (US)
Pages (from-to)187-222
Number of pages36
JournalDuke Mathematical Journal
Volume159
Issue number2
DOIs
StatePublished - Aug 15 2011

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Amenable Group
Lebesgue Space
Finitely Generated Group
Lipschitz
Compression
Exponent

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Amenable groups with very poor compression into Lebesgue spaces. / Austin, Tim.

In: Duke Mathematical Journal, Vol. 159, No. 2, 15.08.2011, p. 187-222.

Research output: Contribution to journalArticle

Austin, Tim. / Amenable groups with very poor compression into Lebesgue spaces. In: Duke Mathematical Journal. 2011 ; Vol. 159, No. 2. pp. 187-222.
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