Coarse equivalences of Euclidean buildings. (With an appendix by Jeroen Schillewaert and Koen Struyve.)

DOI10.1016/j.aim.2013.10.031zbMath1327.51015OpenAlexW2962914400MaRDI QIDQ2445964

Richard M. Weiss, Linus K. H. Kramer

Publication date: 15 April 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2013.10.031

zbMATH Keywords

treesBruhat-Tits buildingsmetric geometryultraproductsEuclidean buildingscoarse equivalencequai-isometric rigidity

Mathematics Subject Classification ID

Metric geometry (51F99) Rigidity results (53C24) Buildings and the geometry of diagrams (51E24) Groups with a (BN)-pair; buildings (20E42) Nonstandard models in mathematics (03H05)

Related Items (7)

Rigidity at infinity of trees and Euclidean buildings ⋮ On the logarithmic coarse structures of Lie groups and hyperbolic spaces ⋮ On panel-regular \(\tilde{A}_2\) lattices ⋮ Polyhedral compactifications. I ⋮ On small abstract quotients of Lie groups and locally compact groups ⋮ Cross ratios on boundaries of symmetric spaces and euclidean buildings ⋮ Strongly transitive actions on Euclidean buildings

Cites Work

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• (Non)-completeness of \(\mathbb R\)-buildings and fixed point theorems
• Affine buildings for dihedral groups
• Gromov's theorem on groups of polynomial growth and elementary logic
• Valuations, trees, and degenerations of hyperbolic structures. I
• A structure theorem for weak buildings of spherical type
• Spherical buildings and the character of the Steinberg representation
• Model theory.
• Buildings of spherical type and finite BN-pairs
• Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings
• Metric characterizations of spherical and Euclidean buildings
• Metric building exercises
• On asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds
• Homogeneous trees are bilipschitz equivalent
• On homomorphisms between generalized polygons
• \(\Lambda\)-buildings and base change functors.
• Reductive groups over a local field
• A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry
• On metrically complete Bruhat–Tits buildings
• On the local structure and the homology of CAT(κ) spaces and euclidean buildings
• The Structure of Affine Buildings. (AM-168)
• Non-discrete Euclidean buildings for the Ree and Suzuki groups
• Affine Λ-Buildings, I
• The Thick Frame of a Weak Twin Building
• Asymptotic Cones and Ultrapowers of Lie Groups

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