Metric Characterizations of Superreflexivity in Terms of Word Hyperbolic Groups and Finite Graphs

Mikhail Ostrovskii

Analysis and Geometry in Metric Spaces (2014)

  • Volume: 2, Issue: 1, page 154-168, electronic only
  • ISSN: 2299-3274

Abstract

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We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups.We compare characterizations of superrefiexivity in terms of diamond graphs and binary trees.We show that there exist sequences of series-parallel graphs of increasing topological complexitywhich admit uniformly bilipschitz embeddings into a Hilbert space, and thus do not characterize superrefiexivity.

How to cite

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Mikhail Ostrovskii. "Metric Characterizations of Superreflexivity in Terms of Word Hyperbolic Groups and Finite Graphs." Analysis and Geometry in Metric Spaces 2.1 (2014): 154-168, electronic only. <http://eudml.org/doc/267138>.

@article{MikhailOstrovskii2014,
abstract = {We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups.We compare characterizations of superrefiexivity in terms of diamond graphs and binary trees.We show that there exist sequences of series-parallel graphs of increasing topological complexitywhich admit uniformly bilipschitz embeddings into a Hilbert space, and thus do not characterize superrefiexivity.},
author = {Mikhail Ostrovskii},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {bi-Lipschitz embedding; diamond graphs; series-parallel graph; superreflexivity;word hyperbolic group; superreflexivity; word hyperbolic group},
language = {eng},
number = {1},
pages = {154-168, electronic only},
title = {Metric Characterizations of Superreflexivity in Terms of Word Hyperbolic Groups and Finite Graphs},
url = {http://eudml.org/doc/267138},
volume = {2},
year = {2014},
}

TY - JOUR
AU - Mikhail Ostrovskii
TI - Metric Characterizations of Superreflexivity in Terms of Word Hyperbolic Groups and Finite Graphs
JO - Analysis and Geometry in Metric Spaces
PY - 2014
VL - 2
IS - 1
SP - 154
EP - 168, electronic only
AB - We show that superreflexivity can be characterized in terms of bilipschitz embeddability of word hyperbolic groups.We compare characterizations of superrefiexivity in terms of diamond graphs and binary trees.We show that there exist sequences of series-parallel graphs of increasing topological complexitywhich admit uniformly bilipschitz embeddings into a Hilbert space, and thus do not characterize superrefiexivity.
LA - eng
KW - bi-Lipschitz embedding; diamond graphs; series-parallel graph; superreflexivity;word hyperbolic group; superreflexivity; word hyperbolic group
UR - http://eudml.org/doc/267138
ER -

References

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