On asymptotic dimension of countable Abelian groups
By J. Smith. 2005
64 citations recorded by the source corpus.
Abstract We compute the asymptotic dimension of the rationals given with an invariant proper metric. We also show that a countable torsion Abelian group taken with an invariant proper metric has asymptotic dimension zero.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/dd70db6bc1a5732a70655517528916bbfe7648d8
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In Geometry and Topology
- Gregory C. Bell
- Alexander Dranishnikov
- K. Fujiwara
- J. Dydak
- J. Smith
- N. Brodskiy
- A. Mitra
- Mark Sh. Levin
In Mathematical Physics
- Gregory C. Bell
- Alexander Dranishnikov
- J. Dydak
- K. Fujiwara
- J. Smith
- N. Brodskiy
- A. Mitra
- Mark Sh. Levin
Citations in the corpus
- Asymptotic Dimension (2007, background): “Taking groups with proper left-invariant metrics can give rise to interesting examples, as pointed out by [88].”
- Asymptotic dimension of discrete groups (2006, background): “1 implies in particular that asdim Q = 1 (see [Sm] for a direct computation).”
- A Hurewicz theorem for the Assouad–Nagata dimension (2006, background): “Notice that Y = ⋃ s∈S gs · Gr is of r-dim(Y ) asdim(Gr) and Y ∪ Gr = G. Corollary 3.14 (Dranishnikov–Smith [4]).”
- Dimension zero at all scales (2006, background): “It is known that a countable group has asymptotic dimension 0 if and only if it is locally finite [21] but we are not aware of any characterization of locally finite countable groups up to coarse equivalence.”
- The asymptotic dimension of a curve graph is finite (2005, background): “Smith [34] showed that every countable group could be endowed with a left-invariant proper metric and that all left-invariant proper metrics are coarsely equivalent.”