This is an announcement for the paper "Metric characterizations of
superreflexivity in terms of word groups and finite graphs" by Mikhail
Ostrovskii.
Abstract: We show that superreflexivity can be characterized in terms
of bilipschitz embeddability of word hyperbolic groups. We compare
characterizations of superreflexivity in terms of diamond graphs and
binary trees. We show that there exist sequences of series-parallel
graphs of increasing topological complexity which admit uniformly
bilipschitz embeddings into a Hilbert space, and thus do not characterize
superreflexivity.
Archive classification: math.MG math.CO math.FA math.GR
Mathematics Subject Classification: Primary: 46B85, Secondary: 05C12,
20F67, 46B07
Submitted from: ostrovsm(a)stjohns.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1312.4627
or
http://arXiv.org/abs/1312.4627
