Direct embeddings of relatively hyperbolic groups with optimal ℓp compression exponent

Direct embeddings of relatively hyperbolic groups with optimal ℓp compression exponent

We prove that for all p > 1, every relatively hyperbolic group has ` p compression exponent equal to the minimum of the exponents of its maximal peripheral subgroups. This improves results of Dadarlat–Guentner and Dreesen. As a first step we give a direct geometric proof that hyperbolic group...

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Detalles Bibliográficos
Autor Principal: Hume, D
Formato: Journal article
Publicado: De Gruyter 2015
Descripción
Summary:We prove that for all p > 1, every relatively hyperbolic group has ` p compression exponent equal to the minimum of the exponents of its maximal peripheral subgroups. This improves results of Dadarlat–Guentner and Dreesen. As a first step we give a direct geometric proof that hyperbolic groups have ` p compression exponent 1, independent of those given by Bonk–Schramm, Buyalo–Dranishnikov–Schroeder, Gal and Tessera.

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