Related papers: Lifting mixing properties by Rokhlin cocycles

We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor--Wiles do not apply. Previous generalizations of these methods have been restricted to situations where the…

We show the following geometric generalization of a classical theorem of W.H. Gottschalk and G.A. Hedlund: a skew action induced by a cocycle of (affine) isometries of a Hilbert space over a minimal dynamics has a continuous invariant…

We show that on an Abelian variety over an algebraically closed field of positive characteristic, the obstruction to lifting an automorphism to an Abelian variety over a field of characteristic zero as a morphism vanishes if and only if it…

The purpose of this article is twofold. On one hand, we reveal the equivalence of shift of finite type between a one-sided shift $X$ and its associated hom tree-shift $\mathcal{T}_{X}$, as well as the equivalence in the sofic shift. On the…

We use former results on geometric local $\varepsilon$-factors over curves in order to prove a factorization result for the determinant of the cohomology of an $\ell$-adic sheaf over an arbitrary proper scheme over a perfect field of…

The circular coordinates algorithm, a key tool in topological data analysis, relies on a theoretically unvalidated lifting step to convert cocycles from a prime field to integer coefficients. We provide a rigorous analysis of this…

We review several techniques that twist an algebra's multiplicative structure. We first consider twists by an automorphism, also known as Zhang twists, and we relate them to 2-cocycle twists of certain bialgebras. We then outline the…

As the second part of a series on linear cocycles over chaotic systems, this paper establishes a "multiple covering principle" that robustly yields positive-entropy ergodic measures supported on fiberwise uniformly bounded orbits. Using…

In this paper we define a Rokhlin property for automorphisms of non-unital C*-algebras and for endomorphisms. We show that the crossed product of a C*-algebra by a Rokhlin automorphism preserves absorption of a strongly self-absorbing…

Let G be a group admitting a non-elementary acylindrical action on a Gromov hyperbolic space (for example, a non-elementary relatively hyperbolic group, or the mapping class group of a closed hyperbolic surface, or Out(F_n) for n>1). We…

This article studies automorphism groups of graph products of arbitrary groups. We completely characterise automorphisms that preserve the set of conjugacy classes of vertex groups as those automorphisms that can be decomposed as a product…

Let $\rho : G \to \operatorname{GL}(V)$ be a rational finite dimensional complex representation of a reductive linear algebraic group $G$, and let $\sigma_1,\sigma_n$ be a system of generators of the algebra of invariant polynomials…

For different classes of measure preserving transformations, we investigate collections of sets that exhibit the property of lightly mixing. Lightly mixing is a stronger property than topological mixing, and requires that a lim inf is…

For a surface semiflow that is a suspension of a \( C^{1+\alpha} \) expanding Markov interval map, we prove that, under the assumptions that the roof function is Lipschitz continuous and not cohomologous to a locally constant function, the…

The covariant holographic entropy conjecture of AdS/CFT relates the entropy of a boundary region R to the area of an extremal surface in the bulk spacetime. This extremal surface can be obtained by a maximin construction, allowing many new…

Two automorphisms of a simple stable AF algebra with a finite dimensional lattice of lower semicontinuous traces are shown to be outer conjugate if they act in the same way on the K-group and the extremal traces are scaled by numbers which…

We consider Holder continuous fiber bunched GL(d,R)-valued cocycles over an Anosov diffeomorphism. We show that two such cocycles are Holder continuously cohomologous if they have equal periodic data, and prove a result for cocycles with…

This article is dedicated to the study of the acylindrical hyperbolicity of automorphism groups of graph products of groups. Our main result is that, if $\Gamma$ is a finite graph which contains at least two vertices and is not a join and…

We establish four results concerning connections between actions on separable C*-algebras with Rokhlin-type properties and absorption of the Jiang-Su algebra Z. For actions of residually finite groups or of the reals which have finite…

Let G be a connected reductive group over an algebraically closed field K of characteristic 0, X an affine symplectic variety equipped with a Hamiltonian action of G. Further, let * be a G-invariant Fedosov star-product on X such that the…