Related papers: Exponential Mixing and Smooth Classification of Co…

We consider Anosov actions of a Lie group $G$ of dimension $k$ on a closed manifold of dimension $k+n.$We introduce the notion of Nil-Anosov action of $G$ (which includes the case where $G$ is nilpotent) and establishes the invariance by…

We study the smooth untwisted cohomology with real coefficients for the action on [SL(2, R) \times \cdot \cdot \cdot \times SL(2, R)]/{\Gamma} by the subgroup of diagonal matrices, where {\Gamma} is an irreducible lattice. In the top…

Let X be a compact manifold with a smooth action of a compact connected Lie group G. Let $L\to X$ be a complex line bundle. Using the Cartan complex for equivariant cohomology, we give a new proof of a theorem of Hattori and Yoshida which…

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of GL_n(C) on the variety of x-nilpotent complex matrices. We obtain a criterion as to whether the action admits a finite number of orbits and specify a…

We study the large-$N$ behavior of random matrix tuples $Y^N = (Y_1^N,\dots,Y_d^N)$ with joint density proportional to $e^{-N^2 V}$ for some convex function $V$ in non-commuting variables satisfying certain bounds on its second derivative.…

We study the ergodicity of non-autonomous discrete dynamical systems with non-uniform expansion. As an application we get that any uniformly expanding finitely generated semigroup action of $C^{1+\alpha}$ local diffeomorphisms of a compact…

We prove a new weak mean ergodic theorem (Theorem A) for 1-cocycles associated to weakly mixing representations of amenable groups. Let $G$ be a finitely generated, discrete, amenable group $G$ which admits a controlled Folner sequence. We…

The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type, in an iterated sense,…

Using the continuous decomposition, we classify strongly free actions of discrete amenable groups on strongly amenable subfactors of type III$_\lambda, 0 < \lambda < 1$. Winsl{\o}w's fundamental homomorphism is a complete invariant. This…

We show that every topological grading of a C*-algebra by a discrete abelian group is implemented by an action of the compact dual group.

Let $G$ and $A$ be objects of a finitely cocomplete homological category $\mathbb C$. We define a notion of an (internal) action of $G$ of $A$ which is functorially equivalent with a point in $\mathbb C$ over $G$, i.e. a split extension in…

Let G be a Lie group acting by diffeomorphisms on a manifold M and consider the image of T[1]G and T[1]M, of G and M respectively, in the category of differential graded manifolds. We show that the obstruction to lift the action of T[1]G on…

An algebraic $\Gamma$-action is an action of a countable group $\Gamma$ on a compact abelian group $X$ by continuous automorphisms of $X$. We prove that any expansive algebraic action of a finitely generated nilpotent group $\Gamma$ on a…

There are several different notions of maximal torus actions on smooth manifolds, in various contexts: symplectic, Riemannian, complex. In the symplectic context, for the so-called isotropy-maximal actions, as well as for the weaker notion…

The "simplicial complexes" and "join" (*) today used within combinatorics aren't the classical concepts, cf. Spanier (1966) p. 108-9, but, exept for \emptyset, complexes having {\emptyset} as a subcomplex resp. \Sigma1 * \Sigma2 := {\sigma1…

The article focuses on a class of second countable groups assembled from profinite and discrete by elementary operations. We focus on a rank associated with these groups that measure their complexity, the decomposition rank. A collection of…

In this paper, we give partial answers to the following questions: Which contact manifolds are contactomorphic to links of isolated complex singularities? Which symplectic manifolds are symplectomorphic to smooth affine varieties? The…

We show that the conjugacy class of an eventually expanding continuous piecewise affine interval map is contained in a smooth codimension 1 submanifold of parameter space. In particular conjugacy classes have empty interior. This is based…

We extend the lattice-theoretic approach of Brandhorst--Cattaneo to classify algebraically trivial actions on the known IHS manifolds, up to deformation and birational conjugacy. In particular, we classify even order algebraically trivial…

We study the parameter space structure of degree $d \ge 3$ one complex variable polynomials as dynamical systems acting on $\C$. We introduce and study {\it straightening maps}. These maps are a natural higher degree generalization of the…