CAT(0) spaces and expanders.

DOI10.1007/s00209-011-0866-yzbMath1284.20043OpenAlexW2105497244MaRDI QIDQ431271

Takefumi Kondo

Publication date: 26 June 2012

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-011-0866-y

zbMATH Keywords

CAT(0) spacesfinitely generated groupsharmonic mapsspectral gapsfixed-point theoremsrandom groupsIzeki-Nayatani invariantsMarkov types

Mathematics Subject Classification ID

Geometric group theory (20F65) Harmonic maps, etc. (58E20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Probabilistic methods in group theory (20P05)

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Random groups have fixed points on $\mathrm{CAT}(0)$ cube complexes ⋮ \(N\)-step energy of maps and the fixed-point property of random groups. ⋮ Old and new challenges in Hadamard spaces ⋮ Uniform estimates of nonlinear spectral gaps ⋮ Fixed-point property of random quotients by plain words. ⋮ An average John theorem ⋮ Expanders with respect to Hadamard spaces and random graphs ⋮ Nonpositive curvature is not coarsely universal ⋮ Group approximation in Cayley topology and coarse geometry. II: Fibred coarse embeddings

Cites Work

• Unnamed Item
• Unnamed Item
• Fixed point property for a CAT(0) space which admits a proper cocompact group action
• CAT(0) spaces on which a certain type of singularity is bounded
• Continuity of a certain invariant of a measure on a CAT(0) space
• Central and \(L^p\)-concentration of 1-Lipschitz maps into \(R\)-trees
• Ramanujan graphs
• Markov chains, Riesz transforms and Lipschitz maps
• On \(L^2\)-cohomology and property (T) for automorphism groups of polyhedral cell complexes
• Random walk in random groups.
• Property (T) and Kazhdan constants for discrete groups
• Girth and Euclidean distortion
• \(\text{CAT}(\kappa)\)-spaces: construction and concentration
• \(N\)-step energy of maps and the fixed-point property of random groups.
• Fixed-point property of random groups.
• Observable concentration of \(mm\)-spaces into spaces with doubling measures
• Markov chains in smooth Banach spaces and Gromov-hyperbolic metric spaces
• Combinatorial harmonic maps and discrete-group actions on Hadamard spaces
• Random groups have fixed points on $\mathrm{CAT}(0)$ cube complexes
• Poincaré inequalities, embeddings, and wild groups
• Groups Not Acting on Manifolds
• Towards a Calculus for Non-Linear Spectral Gaps [Extended Abstract]
• Generalized harmonic maps and representations of discrete groups