Coarse differentiation of quasi-isometries. II: Rigidity for Sol and lamplighter groups
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Publication:1955946
DOI10.4007/annals.2013.177.3.2zbMath1398.22012arXiv0706.0940OpenAlexW2963452823MaRDI QIDQ1955946
David Fisher, Kevin Whyte, Alex Eskin
Publication date: 19 June 2013
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0706.0940
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Expanders and box spaces ⋮ Morse quasiflats. I ⋮ Measure-scaling quasi-isometries ⋮ Metric equivalences of Heintze groups and applications to classifications in low dimension ⋮ Large scale geometry of certain solvable groups. ⋮ Some examples of quasiisometries of nilpotent Lie groups ⋮ Geometry of nontransitive graphs ⋮ Bilipschitz equivalence is not equivalent to quasi-isometric equivalence for finitely generated groups. ⋮ Rigidity of some abelian-by-cyclic solvable group actions on \({\mathbb{T}}^N\) ⋮ Brownian motion on treebolic space: escape to infinity ⋮ A fibered Tukia theorem for nilpotent Lie groups ⋮ Quasisymmetric maps on the boundary of a negatively curved solvable Lie group ⋮ Coarse differentiation and quasi-isometries of a class of solvable Lie groups. I. ⋮ Coarse differentiation and quasi-isometries of a class of solvable Lie groups. II. ⋮ Coarse differentiation of quasi-isometries. I: Spaces not quasi-isometric to Cayley graphs ⋮ Large scale geometry of negatively curved \(\mathbb{R}^n\rtimes\mathbb{R}\) ⋮ Speed of random walks, isoperimetry and compression of finitely generated groups ⋮ Simple groups and irreducible lattices in wreath products ⋮ On the quantitative quasi-isometry problem: transport of Poincaré inequalities and different types of quasi-isometric distortion growth ⋮ Coarse differentiation and quantitative nonembeddability for Carnot groups ⋮ Bilipschitz maps of boundaries of certain negatively curved homogeneous spaces ⋮ Heat flow and quantitative differentiation ⋮ Rigidity of Teichmüller space ⋮ Automata groups generated by Cayley machines of groups of nilpotency class two ⋮ Non-rectifiable Delone sets in SOL and other solvable groups ⋮ Free minimal actions of solvable Lie groups which are not affable ⋮ Embedding certain diffeomorphism groups in the quasi-isometry groups of Euclidean spaces ⋮ Coarse distinguishability of graphs with symmetric growth ⋮ The spheres of Sol
Cites Work
- Coarse differentiation of quasi-isometries. I: Spaces not quasi-isometric to Cayley graphs
- Critical percolation on certain nonunimodular graphs
- Quasi-isometries and rigidity of solvable groups
- Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
- A finitely-presented solvable group with a small quasi-isometry group.
- Lamplighters, Diestel–Leader Graphs, Random Walks, and Harmonic Functions
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