Open AccessAsymptotic dimension and uniform embeddings
Author(s) -
Światosław R. Gal
Publication year - 2008
Publication title -
groups geometry and dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.05
H-Index - 25
eISSN - 1661-7215
pISSN - 1661-7207
DOI - 10.4171/ggd/31
Subject(s) - mathematics , dimension (graph theory) , dimension theory (algebra) , pure mathematics , inductive dimension , minkowski–bouligand dimension , mathematical analysis , fractal dimension , fractal
We show that the type function of a space with finite asymptotic dimensionestimates its Hilbert (or any $l^p$) compression. The method allows to obtainthe lower bound of the compression of the lamplighter group $Z\wr Z$, which hasinfinite asymptotic dimension.Comment: 17 pages, no figure
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