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Asymptotic dimension and uniform embeddings

Research paper by S. R. Gal

Indexed on: 16 Jul '06Published on: 16 Jul '06Published in: Mathematics - Geometric Topology



Abstract

We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The method allows to obtain the lower bound of the compression of the lamplighter group $Z\wr Z$, which has infinite asymptotic dimension.