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Asymptotic dimension

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2008Embargo end date: 01 Jan 2007 English Publisher:Elsevier BVJournal:Topology and its Applications, volume 155, pages 1,265-1,296 (issn: 0166-8641, Copyright policy )Funded by:NSF | Large scale topology of m...
Authors: Mathematics; Statistics, UNC Greensboro Bryan Building, Greensboro, NC 27402, USA ( host institution ); Bell, G. ( author ); Dranishnikov, A. ( author );

doi: 10.1016/j.topol.2008.02.011 , 10.48550/arxiv.math/0703766

arXiv: http://arxiv.org/abs/math/0703766

Asymptotic dimension

Abstract

The asymptotic dimension theory was founded by Gromov in the early 90s. In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension theory of compact metric spaces and applications to the theory of discrete groups.

Added some remarks about coarse equivalence of finitely generated groups.

Related Organizations
Keywords

Discrete group, 20F69, Geometric Topology (math.GT), Group Theory (math.GR), Mathematics - Geometric Topology, 55M10, primary, FOS: Mathematics, Asymptotic dimension, Geometry and Topology, secondary, Dimension, Mathematics - Group Theory, 55M10; 20F69

  • BIP!
    Impact byBIP!
    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 74
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
74
Top 10%
Top 10%
Average
Green
hybrid