Large-scale isoperimetry on locally compact groups and applications

Romain Tessera[1]

  • [1] Vanderbilt University Department of mathematics StevensonCenter, Nashville, TN 37240 United

Séminaire de théorie spectrale et géométrie (2006-2007)

  • Volume: 25, page 179-188
  • ISSN: 1624-5458

Abstract

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We introduce various notions of large-scale isoperimetric profile on a locally compact, compactly generated amenable group. These asymptotic quantities provide measurements of the degree of amenability of the group. We are particularly interested in a class of groups with exponential volume growth which are the most amenable possible in that sense. We show that these groups share various interesting properties such as the speed of on-diagonal decay of random walks, the vanishing of the reduced first -cohomology, or the existence of proper isometric actions on whose orbits are almost quasi-isometries.

How to cite

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Tessera, Romain. "Large-scale isoperimetry on locally compact groups and applications." Séminaire de théorie spectrale et géométrie 25 (2006-2007): 179-188. <http://eudml.org/doc/11223>.

@article{Tessera2006-2007,
abstract = {We introduce various notions of large-scale isoperimetric profile on a locally compact, compactly generated amenable group. These asymptotic quantities provide measurements of the degree of amenability of the group. We are particularly interested in a class of groups with exponential volume growth which are the most amenable possible in that sense. We show that these groups share various interesting properties such as the speed of on-diagonal decay of random walks, the vanishing of the reduced first $L^p$-cohomology, or the existence of proper isometric actions on $L^p$ whose orbits are almost quasi-isometries.},
affiliation = {Vanderbilt University Department of mathematics StevensonCenter, Nashville, TN 37240 United},
author = {Tessera, Romain},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {amenable; -isoperimetric profile; elementary solvable group; geometrically elementary solvable group; random walk; -cohomology},
language = {eng},
pages = {179-188},
publisher = {Institut Fourier},
title = {Large-scale isoperimetry on locally compact groups and applications},
url = {http://eudml.org/doc/11223},
volume = {25},
year = {2006-2007},
}

TY - JOUR
AU - Tessera, Romain
TI - Large-scale isoperimetry on locally compact groups and applications
JO - Séminaire de théorie spectrale et géométrie
PY - 2006-2007
PB - Institut Fourier
VL - 25
SP - 179
EP - 188
AB - We introduce various notions of large-scale isoperimetric profile on a locally compact, compactly generated amenable group. These asymptotic quantities provide measurements of the degree of amenability of the group. We are particularly interested in a class of groups with exponential volume growth which are the most amenable possible in that sense. We show that these groups share various interesting properties such as the speed of on-diagonal decay of random walks, the vanishing of the reduced first $L^p$-cohomology, or the existence of proper isometric actions on $L^p$ whose orbits are almost quasi-isometries.
LA - eng
KW - amenable; -isoperimetric profile; elementary solvable group; geometrically elementary solvable group; random walk; -cohomology
UR - http://eudml.org/doc/11223
ER -

References

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