Group cocycles and the ring of affiliated operators
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Publication:639839
DOI10.1007/s00222-011-0310-2zbMath1227.22003arXiv0708.4327OpenAlexW2156896240WikidataQ61677685 ScholiaQ61677685MaRDI QIDQ639839
Publication date: 11 October 2011
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0708.4327
(L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Group theory and generalizations (20-XX) Topological groups, Lie groups (22-XX)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The rank gradient from a combinatorial viewpoint.
- Normalisers in limit groups.
- Amalgamated free products of weakly rigid factors and calculation of their symmetry groups
- Isometric group actions on Banach spaces and representations vanishing at infinity
- \(L^2\)-Betti numbers of one-relator groups.
- \(L^{2}\)-rigidity in von Neumann algebras
- \(L_ 2\)-cohomology and group cohomology
- The maximal ring of quotients of a finite von Neumann algebra
- De Rham-Hodge theory for \(L^2\)-cohomology of infinite coverings
- Group cohomology, harmonic functions and the first \(L^ 2\)-Betti number
- On the K- and L-theory of the algebra of operators affiliated to a finite von Neumann algebra
- Limit groups as limits of free groups.
- Some groups whose reduced \(C^*\)-algebra is simple
- Theory of operator algebras. II
- Diophantine geometry over groups. I: Makanin-Razborov diagrams
- \(\ell^2\) invariants of equivalence relations and groups
- On the first \(L^p\)-cohomology of discrete groups.
- \(L^{2}\)-cohomology for von Neumann algebras
- Cocycle and orbit equivalence superrigidity for malleable actions of \(w\)-rigid groups
- Strongly 1-bounded von Neumann algebras
- Vanishing and non-vanishing for the first \(L^p\)-cohomology of groups.
- Semi-continuity of the first \(\ell^2\)-Betti number on the space of finitely generated groups.
- Strong rigidity of \(\text{II}_1\) factors arising from malleable actions of \(w\)-rigid groups. I
- Strong rigidity of \(\text{II}_1\) factors arising from malleable actions of \(w\)-rigid groups. II
- The fundamental group of a surface, and a theorem of Schreier
- Subgroup properties of fully residually free groups
- Note on a Theorem of Schreier
- Free entropy dimension in amalgamated free products
- L2-Betti Numbers and Non-Unitarizable Groups without Free Subgroups
- Subrelations of ergodic equivalence relations
- Metrically Complete Regular Rings
- Division Rings and Group von Neumann Algebras
- On Certain Finitely Generated Subgroups of Groups Which Split
- Approximating L2‐invariants and the Atiyah conjecture
- ON GROWTH OF GROUPS WITH FEW RELATORS
- Limit groups, positive-genus towers and measure-equivalence
- SOME COMPUTATIONS OF 1-COHOMOLOGY GROUPS AND CONSTRUCTION OF NON-ORBIT-EQUIVALENT ACTIONS
- A generalization of the Lyndon–Hochschild–Serre spectral sequence with applications to group cohomology and decompositions of groups
- Intersections of Finitely Generated Subgroups in Free Products
- Examples of groups that are measure equivalent to the free group
- Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu