W* and C*-superrigidity for product groups

Daniel Drimbe, PhD

We provide a new large class C_AFP of amalgamated free products, for which the product rigidity result of Chifan-de Santiago-Sinclair holds: if G₁, …, Gₙ ∈ C_AFP and H is any group such that L(G₁ × ··· × Gₙ) ≅ L(H), then there exists a product decomposition H = H₁ × ··· × Hₙ such that L(Hᵢ) is stably isomorphic to L(Gᵢ) for every 1 ≤ i ≤ n. Since the class C_AFP contains W*- and C*-superrigid groups, we obtain new examples of product groups that are both W*- and C*-superrigid. This is based on a joint work with Jakub Curda.

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