Deformation and rigidity for group actions and von Neumann algebras

2007/05/15 by Sorin Popa · 2 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Rigidity (electromagnetism) #Ergodic theory #Mathematics #Von Neumann architecture #Pure mathematics #Equivalence (formal languages) #Physics #Quantum mechanics

paper · doi:10.4171/022-1/18

openalex publication_date 2007/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/15

Abstract

We present some recent rigidity results for von Neumann algebras (II1 factors) and equivalence relations arising from measure preserving actions of groups on probability spaces which satisfy a combination of deformation and rigidity properties. This includes strong rigidity results for factors with calculation of their fundamental group and cocycle superrigidity for actions with applications to orbit equivalence ergodic theory.

Citations

• Tensor products of operator algebras
• On Groups of Measure Preserving Transformations. I
• Multipliers of the Fourier Algebras of Some Simple Lie Groups and Their Discrete Subgroups
• Gromov's Measure Equivalence and Rigidity of Higher Rank Lattices
• Orbit equivalence rigidity and bounded cohomology
• On Rings of Operators
• On the Superrigidity of Malleable Actions with Spectral Gap

Cited by

• Acylindrically hyperbolic groups
• Infinite conjugacy class property [wikipedia]

Related

• Rigidity for von Neumann algebras
• Rigidity results for von Neumann algebras arising from mixing extensions of profinite actions of groups on probability spaces
• Classification and rigidity for von Neumann algebras
• Rigidity for equivalence relations on homogeneous spaces
• Approximate equivalence of actions