Embedding relatively hyperbolic groups in products of trees.

DOI10.2140/agt.2013.13.2261zbMath1286.20054arXiv1207.3008OpenAlexW2030130248MaRDI QIDQ1954182

Alessandro Sisto, John M. Mackay

Publication date: 20 June 2013

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.3008

zbMATH Keywords

asymptotic dimensionrelatively hyperbolic groupsproducts of treesperipheral subgroups

Mathematics Subject Classification ID

Geometric group theory (20F65) Metric spaces, metrizability (54E35) Topological methods in group theory (57M07) Asymptotic properties of groups (20F69) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Hyperbolic groups and nonpositively curved groups (20F67) Dimension theory in general topology (54F45) Groups acting on trees (20E08)

Related Items

Hyperplanes of Squier's cube complexes ⋮ Relatively hyperbolic groups with fixed peripherals ⋮ Extending higher-dimensional quasi-cocycles ⋮ Asymptotic dimension of graphs of groups and one-relator groups ⋮ Constructing group actions on quasi-trees and applications to mapping class groups ⋮ Burghelea conjecture and asymptotic dimension of groups ⋮ On the asymptotic dimension of the curve complex

Cites Work

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• Projections and relative hyperbolicity.
• Cohomological approach to asymptotic dimension.
• Assouad-Nagata dimension via Lipschitz extensions
• On exactness and isoperimetric profiles of discrete groups
• On asymptotic Assouad-Nagata dimension
• Elements of asymptotic geometry
• Constructing group actions on quasi-trees and applications to mapping class groups
• On asymptotic dimension of amalgamated products and right-angled Coxeter groups.
• Embeddings of hyperbolic groups into products of binary trees
• Dehn filling in relatively hyperbolic groups.
• Combination of convergence groups.
• On asymptotic dimension of groups acting on trees.
• On asymptotic dimension of groups
• The large scale geometry in nilpotent Lie groups
• Contracting elements and random walks
• Assouad-Nagata dimension of connected Lie groups
• Embedding mapping class groups into a finite product of trees
• Asymptotic dimension and uniform embeddings.
• Tree-graded spaces and asymptotic cones of groups. (With an appendix by Denis Osin and Mark Sapir).
• Direct embeddings of relatively hyperbolic groups with optimal \(\ell^p\) compression exponent
• 3-manifold groups
• Embedding of hyperbolic spaces in the product of trees
• Embedding universal covers of graph manifolds in products of trees
• RELATIVELY HYPERBOLIC GROUPS
• Graph manifolds with boundary are virtually special
• A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory
• A Hurewicz theorem for the Assouad-Nagata dimension
• Asymptotic cones and Assouad-Nagata dimension
• Criteria for virtual fibering
• Dimension of asymptotic cones of Lie groups
• Graph manifolds with non-empty boundary are covered by surface bundles
• Virtual cubulation of nonpositively curved graph manifolds
• Dimensions of locally and asymptotically self-similar spaces
• Hyperbolic dimension of metric spaces
• Asymptotic dimension of a hyperbolic space and capacity dimension of its boundary at infinity
• Relatively hyperbolic groups