arXiv subjects
Publications and source records attributed to Bram Verjans.
We prove the first orbit equivalence superrigidity results for actions of type III$_λ$ when $λ\neq 1$. These actions arise as skew products of actions of dense subgroups of $SL(n,\mathbb{R})$ on the sphere $S^{n-1}$ and they can have any prescribed associated flow.
We prove rigidity and classification results for type III factors given by nonsingular Bernoulli actions of the free groups and more general free product groups. This includes a large family of nonisomorphic Bernoulli crossed products of type III$_1$ that cannot be distinguished by Connes $τ$-invariant. These are the first such classification results beyond the well studied probability measure preserving case.