Asymptotic Dimension

2007/03/26 by Bell, G., Dranishnikov, A. · 7 citations
#20F69 #55M10 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0703766

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.

Cited by

• Nerve-type and invariance theorems for asymptotic dimension
• A Hurewicz-type theorem for quasimorphisms of countable approximate groups
• Boundary dynamics, triple transitivity, and mixed identities in weakly hyperbolic groups
• String graphs are quasi-isometric to planar graphs
• On the Coarse Lusternik-Schnirelmann Category of Groups
• Induced Minors, Asymptotic Dimension, and Baker's Technique
• Geometric models and asymptotic dimension for infinite-type surface mapping class groups

Related

• A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory
• Dynamic Asymptotic Dimension: relation to dynamics, topology, coarse geometry, and C^*-algebras
• Semigroup-controlled asymptotic dimension
• Asymptotic dimension of one relator groups
• On asymptotic property C