Dimension and Fundamental Groups of Asymptotic Cones

DOI10.1112/S0024610799007127zbMath0922.20047OpenAlexW2163178997MaRDI QIDQ4354244

José Burillo

Publication date: 15 September 1997

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

Full work available at URL: https://doi.org/10.1112/s0024610799007127

zbMATH Keywords

asymptotic coneshyperbolic spacesfundamental groupsBaumslag-Solitar groupsdimension theoremsultrametric spacesexponential Dehn functionsmetrically parallel fibers

Mathematics Subject Classification ID

Topological methods in group theory (57M07) Other groups related to topology or analysis (20F38) Fundamental group, presentations, free differential calculus (57M05) Dimension theory in general topology (54F45) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34)

Related Items (12)

Asymptotic geometry of the mapping class group and Teichmüller space ⋮ Asymptotic cones of HNN extensions and amalgamated products. ⋮ Asymptotic cones and Assouad-Nagata dimension ⋮ Dimension of asymptotic cones of Lie groups ⋮ Local topological properties of asymptotic cones of groups. ⋮ CYCLIC SUBGROUPS ARE QUASI-ISOMETRICALLY EMBEDDED IN THE THOMPSON–STEIN GROUPS ⋮ On the local structure and the homology of CAT(κ) spaces and euclidean buildings ⋮ On the quasi-isometric and bi-Lipschitz classification of 3D Riemannian Lie groups ⋮ Fundamental group of asymptotic cones of abelian-by-cyclic groups. ⋮ On quadratic Dehn functions. ⋮ The homeomorphism problem for closed 3-manifolds ⋮ Lacunary hyperbolic groups. With an appendix by Michael Kapovich and Bruce Kleiner.

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