Compression functions of uniform embeddings of groups into Hilbert and Banach spaces

@inproceedings{Arzhantseva2009CompressionFO,
  title={Compression functions of uniform embeddings of groups into Hilbert and Banach spaces},
  author={Goulnara N. Arzhantseva and Cornelia Dructu and Mark V. Sapir},
  year={2009}
}
We construct finitely generated groups with arbitrary prescribed Hilbert space compression α ∈ [0, 1]. For a large class of Banach spaces E (including all uniformly convex Banach spaces), the E–compression of these groups coincides with their Hilbert space compression. Moreover, the groups that we construct have asymptotic dimension at most 2, hence they are exact. In particular, the first examples of groups that are uniformly embeddable into a Hilbert space (moreover, of finite asymptotic… CONTINUE READING

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