McDuff superrigidity for group II₁ factors

2025/11/28 by Juan Felipe Ariza Mejía, Mejía, Juan Felipe Ariza, Ionuţ Chifan +5
Mathematics · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2511.23123

Abstract

Developing new techniques at the interface of geometric group theory and von Neumann algebras, we identify the first examples of ICC groups G whose von Neumann algebras are McDuff and exhibit a new rigidity phenomenon, termed McDuff superrigidity: an arbitrary group H satisfying L(H)≅ L(G) decomposes as H ≅ G× A for an ICC amenable group A.

Citations

• Relative solidity for biexact groups in measure equivalence
• Rigidity results for group von Neumann algebras with diffuse center
• Wreath-like products of groups and their von Neumann algebras III: Embeddings
• Biexact von Neumann algebras
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• Wreath-like products of groups and their von Neumann algebras I: W^∗-superrigidity
• W^* and C^*-superrigidity results for coinduced groups
• Von Neumann algebras of Thompson-like groups from cloning systems
• Some rigidity results for II₁ factors arising from wreath products of\n property (T) groups
• A class of superrigid group von Neumann algebras
• Rigidity results for wreath product II₁ factors
• Dehn filling in relatively hyperbolic groups
• Peripheral fillings of relatively hyperbolic groups
• The Inner Amenability of the Generalized Thompson Group
• Strong Rigidity of II₁ Factors Arising from Malleable Actions of w-Rigid Groups, I
• Sharp phase transition theorems for hyperbolicity of random groups

Related

• New examples of W^* and C^*-superrigid groups
• Strong Rigidity of II₁ Factors Arising from Malleable Actions of w-Rigid Groups, I
• W*-superrigidity for groups with infinite center
• W^*-superrigidity for property (T) groups with infinite center
• Strongly solid group factors which are not interpolated free group factors