Quasi-isometric classification of non-geometric 3-manifold groups

DOI10.1515/CRELLE.2011.143zbMath1252.57001arXiv1001.0212MaRDI QIDQ2910996

Walter D. Neumann, Jason A. Behrstock

Publication date: 12 September 2012

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.0212

zbMATH Keywords

labeled graphquasi-isometric classificationcommensurablenon-geometric \(3\)-manifold groups

Mathematics Subject Classification ID

General low-dimensional topology (57M99) Fundamental group, presentations, free differential calculus (57M05)

Related Items

Imitator homomorphisms for special cube complexes ⋮ Leighton's theorem : extensions, limitations and quasitrees ⋮ Quasi-isometries between groups with two-ended splittings ⋮ On the quantitative quasi-isometry problem: transport of Poincaré inequalities and different types of quasi-isometric distortion growth ⋮ On Leighton's graph covering theorem ⋮ Local topological rigidity of nongeometric 3-manifolds ⋮ Revisiting Leighton’s theorem with the Haar measure ⋮ Acylindrical hyperbolicity of groups acting on trees ⋮ Two generalisations of Leighton's theorem (with an appendix by Giles Gardam and Daniel J. Woodhouse)

Cites Work

• On Leighton's graph covering theorem
• Quasi-isometries preserve the geometric decomposition of Haken manifolds
• Peripheral fillings of relatively hyperbolic groups.
• Dehn filling in relatively hyperbolic groups.
• Finite common coverings of graphs
• The quasi-isometry classification of rank one lattices
• Quasi-isometric classification of graph manifold groups.
• Commensurability and virtual fibration for graph manifolds
• Abelian Subgroup Separability of Haken 3-Manifolds and Closed Hyperbolic n -Orbifolds