Actions of picture groups on CAT(0) cubical complexes.

DOI10.1007/s10711-004-1530-zzbMath1139.20038OpenAlexW2028251453MaRDI QIDQ1775140

Daniel Scott Farley

Publication date: 4 May 2005

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-004-1530-z

zbMATH Keywords

Haagerup propertydiagram groupsCAT(0) cubical complexesa-T-menabilitypicture groupsRichard Thompson groups

Mathematics Subject Classification ID

Geometric group theory (20F65) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (16)

CAT(0) cube complexes with flat hyperplanes ⋮ Fixed points and amenability in non-positive curvature ⋮ No quasi-isometric rigidity for proper actions on CAT(0) cube complexes ⋮ Semi-simple actions of the Higman-Thompson groups \(T_n\) on finite-dimensional CAT(0) spaces ⋮ The simplicial boundary of a CAT(0) cube complex ⋮ On embeddings of CAT(0) cube complexes into products of trees via colouring their hyperplanes ⋮ Hyperbolic and cubical rigidities of Thompson's group \(V\) ⋮ Quasiautomorphism groups of type \(F_\infty\) ⋮ Thompson's group \(\mathcal T\) is the orientation-preserving automorphism group of a cellular complex ⋮ The infinite associahedron and R. J. Thompson's group \(T\) ⋮ On the wgsc and qsf tameness conditions for finitely presented groups ⋮ Local similarities and the Haagerup property. With an appendix by Daniel S. Farley. ⋮ Divergence functions of Thompson groups ⋮ Rearrangement groups of fractals ⋮ On the Haagerup and Kazhdan properties of R. Thompson's groups ⋮ On groups whose actions on finite-dimensional CAT(0) spaces have global fixed points

Cites Work

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• Diagram groups and directed 2-complexes: homotopy and homology.
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• Central sequences in the factor associated with Thomson's group \(F\)
• Introductory notes on Richard Thompson's groups
• Groups acting on \(\text{CAT}(0)\) cube complexes
• Finiteness and CAT(0) properties of diagram groups.
• On theories with a combinatorial definition of 'equivalence'
• Moyennabilité intérieure du groupe F de Thompson
• Diagram groups
• RIGIDITY PROPERTIES OF DIAGRAM GROUPS
• Ends of Group Pairs and Non-Positively Curved Cube Complexes
• On subgroups of R. Thompson's group $ F$ and other diagram groups
• \(E\)-theory and \(KK\)-theory for groups which act properly and isometrically on Hilbert space

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