Related papers: Full factors, bicentralizer flow and approximately…

We prove that many, but not all injective factors arise as crossed products by nonsingular Bernoulli actions of the group $\mathbb{Z}$. We obtain this result by proving a completely general result on the ergodicity, type and Krieger's…

We study R-covered foliations of 3-manifolds from the point of view of their transverse geometry. For an R-covered foliation in an atoroidal 3-manifold M, we show that M-tilde can be partially compactified by a canonical cylinder S^1_univ x…

We prove that there exist uncountably many separable II$_1$ factors whose ultrapowers (with respect to arbitrary ultrafilters) are non-isomorphic. In fact, we prove that the families of non-isomorphic II$_1$ factors originally introduced by…

In this paper we consider the following problem: When are the preduals of two hyperfinite (=injective) factors $\M$ and $\N$ (on separable Hilbert spaces) cb-isomorphic (i.e., isomorphic as operator spaces)? We show that if $\M$ is…

Let $M$ be a closed, negatively curved Riemannian manifold of dimension $n \neq 4, 8$ with strictly $1/4$-pinched sectional curvature. We prove, that if the frame flow is ergodic and the sum of its unstable and stable bundles together with…

We show that if a non-amenable, quasi-transitive, unimodular graph $G$ has all degrees even then it has a factor-of-iid balanced orientation, meaning each vertex has equal in- and outdegree. This result involves extending earlier…

In \cite{Ioana:vNsuperrigidity}, Ioana introduced three new invariants of type II$_1$ factors: the one-sided fundamental group, the endomorphism semigroup and the set of right-finite bimodules. In \cite{Ioana:vNsuperrigidity}, he does not…

We prove automatic continuity theorems for "decomposable" or "local" linear transformations between certain natural subspaces of operator algebras. The transformations involved are not algebra homomorphisms but often are module…

We introduce a quite large class of functions (including the exponential function and the power functions with exponent greater than one), and show that for any element $f$ of this function class, a self-adjoint element $a$ of a…

We study the von Neumann algebra, generated by the regular representations of the infinite-dimensional nilpotent group $B_0^{\mathbb Z}$. In [14] a condition have been found on the measure for the right von Neumann algebra to be the…

In this work we completely classify $C^\infty$ conjugacy for conservative partially hyperbolic diffeomorphisms homotopic to a linear Anosov automorphism on the 3-torus by its center foliation behavior. We prove that the uniform version of…

We show that if $G$ is a a countable amenable group with the comparison property, and $X$ is a strongly irreducible $G$-shift satisfying certain aperiodicity conditions, then $X$ factors onto the full $G$-shift over $N$ symbols, so long as…

For any abstract subfactor planar algebra $P$, there exists a finite index extremal subfactor $M_0 \subset M_1$ with $P$ as its standard invariant. In this paper, we classify the automorphism group of a bipartite graph planar algebra, and…

Let $M$ be a closed manifold that admits a self-cover $p:M \to M$ of degree >1. We say p is strongly regular if all its iterates are regular covers. In this case, we establish an algebraic structure theorem for the fundamental group of $M$:…

A wide and natural class of closed currents - which are differences of positive closed currents - can be constructed by pulling back smooth closed forms using rational maps. These currents are very singular in general, and hence defining…

Let a countable amenable group G acts freely and ergodically on a Lebesgue space (X,mu), preserving the measure mu. If T is an automorphism of the equivalence relation defined by G then T can be extended to an automorphism alpha_T of the…

The sets of $\cB$-free integers are considered with respect to (reversing) symmetries. It is well known that, for a large class of them, the centraliser of the associated $\cB$-free shift (otherwise known as its automorphism group) is…

We show that the following operator algebras have hyperarithmetic theory: the hyperfinite II$_1$ factor $\mathcal R$, $L(\Gamma)$ for $\Gamma$ a finitely generated group with solvable word problem, $C^*(\Gamma)$ for $\Gamma$ a finitely…

For any finite dimensional C^*-algebra A, we give an endomorphism \Phi of the hyperfinite II_1 factor R of finite Jones index such that: for all k \in \mathbb {N}, \Phi^k (R)' \cap R= \otimes^k A. The Jones index [R: \Phi (R)]= (rank…

We consider a class of partially hyperbolic diffeomorphisms introduced in [BFP] which is open and closed and contains all known examples. If in addition the diffeomorphism is non-wandering, then we show it is accessible unless it contains a…