On the Lp-distortion of finite quotients of amenable groups

Romain Tessera

doi:10.1007/s11117-011-0136-6

On the L^p-distortion of finite quotients of amenable groups

Romain Tessera

CNRS UMR 5669, 'Unité de Mathématiques Pures et Appliquées' and project-team Inria NUMED, Ecole Normale Supérieure de Lyon

Research output: Contribution to journal › Article › peer-review

Abstract

We study the L^p-distortion of finite quotients of amenable groups. In particular, for every 2 ≤ p < ∞, we prove that the ℓ^p-distortions of the groups C₂ C_n and C_2n ⋊ are in Θ((log n)^1/p), and that the ℓ^p-distortion of C_n² ⋊_A Z, where A is the matrix, is in Θ ((log log n)^1/p.

Original language	English
Pages (from-to)	633-640
Number of pages	8
Journal	Positivity
Volume	16
Issue number	4
DOIs	https://doi.org/10.1007/s11117-011-0136-6
Publication status	Published - 1 Dec 2012
Externally published	Yes

Keywords

Distortion of Bilipschitz embeddings
Finite metric spaces
Isometric group actions
Isoperimetry

Access to Document

10.1007/s11117-011-0136-6

Cite this

@article{2996dd22d3e74e8dadf6283a9c569ed7,

title = "On the Lp-distortion of finite quotients of amenable groups",

abstract = "We study the Lp-distortion of finite quotients of amenable groups. In particular, for every 2 ≤ p < ∞, we prove that the ℓp-distortions of the groups C2 Cn and C2n ⋊ are in Θ((log n)1/p), and that the ℓp-distortion of Cn2 ⋊A Z, where A is the matrix, is in Θ ((log log n)1/p.",

keywords = "Distortion of Bilipschitz embeddings, Finite metric spaces, Isometric group actions, Isoperimetry",

author = "Romain Tessera",

year = "2012",

month = dec,

day = "1",

doi = "10.1007/s11117-011-0136-6",

language = "English",

volume = "16",

pages = "633--640",

journal = "Positivity",

issn = "1385-1292",

number = "4",

}

TY - JOUR

T1 - On the Lp-distortion of finite quotients of amenable groups

AU - Tessera, Romain

PY - 2012/12/1

Y1 - 2012/12/1

N2 - We study the Lp-distortion of finite quotients of amenable groups. In particular, for every 2 ≤ p < ∞, we prove that the ℓp-distortions of the groups C2 Cn and C2n ⋊ are in Θ((log n)1/p), and that the ℓp-distortion of Cn2 ⋊A Z, where A is the matrix, is in Θ ((log log n)1/p.

AB - We study the Lp-distortion of finite quotients of amenable groups. In particular, for every 2 ≤ p < ∞, we prove that the ℓp-distortions of the groups C2 Cn and C2n ⋊ are in Θ((log n)1/p), and that the ℓp-distortion of Cn2 ⋊A Z, where A is the matrix, is in Θ ((log log n)1/p.

KW - Distortion of Bilipschitz embeddings

KW - Finite metric spaces

KW - Isometric group actions

KW - Isoperimetry

UR - https://www.scopus.com/pages/publications/84869123661

U2 - 10.1007/s11117-011-0136-6

DO - 10.1007/s11117-011-0136-6

M3 - Article

AN - SCOPUS:84869123661

SN - 1385-1292

VL - 16

SP - 633

EP - 640

JO - Positivity

JF - Positivity

IS - 4

ER -

On the L^p-distortion of finite quotients of amenable groups

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this