A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory

DOI10.1090/S0002-9947-06-04088-8zbMath1117.20032arXivmath/0407431OpenAlexW1503681158MaRDI QIDQ3420340

Gregory C. Bell, Alexander N. Dranishnikov

Publication date: 1 February 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407431

zbMATH Keywords

nilpotent groupspolycyclic groupsasymptotic dimensionLipschitz mappingsnervesgeodesic metric spacesHirsch lengthsHurewicz-type theoremuniformly bounded covers

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Geometric group theory (20F65) Topological methods in group theory (57M07) Asymptotic properties of groups (20F69) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Dimension theory in algebraic topology (55M10) Groups acting on trees (20E08)

Related Items (30)

COARSE COHERENCE OF METRIC SPACES AND GROUPS AND ITS PERMANENCE PROPERTIES ⋮ Higson compactification and dimension raising ⋮ On exactness and isoperimetric profiles of discrete groups ⋮ On asymptotic Assouad-Nagata dimension ⋮ On macroscopic dimension of universal coverings of closed manifolds ⋮ Dimension of compact metric spaces ⋮ Constructing group actions on quasi-trees and applications to mapping class groups ⋮ Asymptotic cones and Assouad-Nagata dimension ⋮ The integral Novikov conjectures for linear groups containing torsion elements ⋮ On the dimension growth of groups. ⋮ Hyperplane arrangements in negatively curved manifolds and relative hyperbolicity. ⋮ Finite asymptotic dimension for CAT(0) cube complexes. ⋮ Asymptotic and Assouad–Nagata dimension of finitely generated groups and their subgroups ⋮ Classification of metric spaces with infinite asymptotic dimension ⋮ Extension properties of asymptotic property C and finite decomposition complexity ⋮ Embedding relatively hyperbolic groups in products of trees. ⋮ An alternative definition of coarse structures ⋮ Asymptotic dimension ⋮ Speed of random walks, isoperimetry and compression of finitely generated groups ⋮ Higher invariants in noncommutative geometry ⋮ On asymptotic dimension of amalgamated products and right-angled Coxeter groups. ⋮ The impact of Pontryagin and Bohr functors on large-scale properties of locally compact abelian groups ⋮ On the stability of asymptotic property C for products and some group extensions ⋮ Assouad-Nagata dimension of nilpotent groups with arbitrary left invariant metrics ⋮ On modules over infinite group rings ⋮ The Novikov conjecture ⋮ Buildings have finite asymptotic dimension. ⋮ Unnamed Item ⋮ Geodesic spaces of low Nagata dimension ⋮ Preserving coarse properties

Cites Work

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• The Novikov conjecture for groups with finite asymptotic dimension
• On asymptotic dimension of groups acting on trees.
• On asymptotic dimension of groups
• Universal spaces for asymptotic dimension
• On homological coherence of discrete groups
• Asymptotic topology
• Asymptotic properties of groups acting on complexes
• On a formula for the asymptotic dimension of free products

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