Geodesic
Metric Characterizations of Superreflexivity in Terms of Word Hyperbolic Groups and Finite Graphs
Analysis and Geometry in Metric Spaces, Tome 2 (2014) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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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.
Mots-clés : bi-Lipschitz embedding, diamond graphs, series-parallel graph, superreflexivity;word hyperbolic group 
@article{AGMS_2014_2_1_a13,
     author = {Ostrovskii, Mikhail},
     title = {Metric {Characterizations} of {Superreflexivity} in {Terms} of {Word} {Hyperbolic} {Groups} and {Finite} {Graphs}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2014},
     volume = {2},
     number = {1},
     zbl = {1318.46010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2014_2_1_a13/}
}
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Ostrovskii, Mikhail. Metric Characterizations of Superreflexivity in Terms of Word Hyperbolic Groups and Finite Graphs. Analysis and Geometry in Metric Spaces, Tome 2 (2014) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2014_2_1_a13/