\(N\)-step energy of maps and the fixed-point property of random groups.

DOI10.4171/GGD/171zbMath1337.20042arXiv1210.5829MaRDI QIDQ1932133

Shin Nayatani, Takefumi Kondo, Hiroyasu Izeki

Publication date: 17 January 2013

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.5829

zbMATH Keywords

finitely generated groupsexpandersEuclidean buildingsrandom groupsCAT(0)-spacesfixed-point propertyenergy of mapsWang invariants

Mathematics Subject Classification ID

Geometric group theory (20F65) Fixed-point theorems on manifolds (58C30) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Probabilistic methods in group theory (20P05)

Related Items (8)

Random groups have fixed points on $\mathrm{CAT}(0)$ cube complexes ⋮ Random groups, random graphs and eigenvalues of \(p\)-Laplacians ⋮ Old and new challenges in Hadamard spaces ⋮ Isometric group actions with vanishing rate of escape on \(\mathrm{CAT}(0)\) spaces ⋮ CAT(0) spaces and expanders. ⋮ Uniform estimates of nonlinear spectral gaps ⋮ Fixed-point property of random quotients by plain words. ⋮ Expanders with respect to Hadamard spaces and random graphs

Cites Work

• CAT(0) spaces and expanders.
• Ramanujan graphs
• Gradient flows on nonpositively curved metric spaces and harmonic maps
• Random walk in random groups.
• Addendum to ``Random walk in random groups by M. Gromov.
• Sobolev spaces and harmonic maps for metric space targets
• Fixed-point property of random groups.
• The nonexistence of certain generalized polygons
• Combinatorial harmonic maps and discrete-group actions on Hadamard spaces
• Poincaré inequalities, embeddings, and wild groups
• Generalized harmonic maps and representations of discrete groups
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