Actions of $\mathbb {F}_\infty $ whose II$_1$ factors and orbit equivalence relations have prescribed fundamental group
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Publication:3584351
DOI10.1090/S0894-0347-09-00644-4zbMath1202.46069arXiv0803.3351MaRDI QIDQ3584351
Publication date: 27 August 2010
Published in: Journal of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0803.3351
outer automorphism groupdeformation/rigidityrigid actionsactions of free groupsfundamental group of II\(_1\) equivalence relationsfundamental group of II\(_1\) factors
General theory of von Neumann algebras (46L10) General groups of measure-preserving transformations (28D15) Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations (37A20) Classification of factors (46L36)
Related Items (16)
A note on trace scaling actions and fundamental groups of C$^*$-algebras ⋮ Group measure space decomposition of \(\text{II}_{1}\) factors and \(\text W^{*}\)-superrigidity ⋮ Explicit examples of equivalence relations and II₁ factors with prescribed fundamental group and outer automorphism group ⋮ Free product actions with relative property (T) and trivial outer automorphism groups ⋮ Fundamental group of simple \(C^{*}\)-algebras with unique trace. II ⋮ \(\operatorname{SL}_2\) representations and relative property (T) ⋮ Rigidity for group actions on homogeneous spaces by affine transformations ⋮ \(W^\ast\)-representations of subfactors and restrictions on the Jones index ⋮ Fundamental group of uniquely ergodic Cantor minimal systems ⋮ A classification of all finite index subfactors for a class of group-measure space II\(_{1}\) factors ⋮ ON FUNDAMENTAL GROUPS OF TENSOR PRODUCT FACTORS ⋮ Orbit equivalence and Borel reducibility rigidity for profinite actions with spectral gap ⋮ II1 FACTORS AND EQUIVALENCE RELATIONS WITH DISTINCT FUNDAMENTAL GROUPS ⋮ Relative property (T) for the subequivalence relations induced by the action of SL\(_2(\mathbb Z)\) on \(\mathbb T^2\) ⋮ Turbulence and Araki-Woods factors ⋮ Unique Cartan decomposition for \(\mathrm{II}_1\) factors arising from arbitrary actions of free groups
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