Related papers: Global rigidity of smooth ${\mathbb Z}\ltimes_\lam…

Extending well-known results on surfaces, we give bounds on the cohomological action of automorphisms of compact K\"ahler threefolds. More precisely, if the action is virtually unipotent we prove that the norm of $(f^n)^*$ grows at most as…

Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…

We consider the dependence of the recently proposed action/complexity duality conjecture on time and on the underlying topology of the bulk spacetime. For the former, we compute the dependence of the CFT complexity on a boundary temporal…

We prove trivialization of the first cohomology with coefficients in smooth vector fields, for a class of $\mathbb Z^2$ parabolic actions on $(SL(2, \mathbb R)\times SL(2, \mathbb R))/\Gamma$, where the lattice $\Gamma$ is irreducible and…

Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We…

We derive the flow equation for the gravitational effective average action in an $f(R)$ truncation on hyperbolic spacetimes using the exponential parametrization of the metric. In contrast to previous works on compact spaces, we are able to…

Given an automorphism $\phi:\Gamma\to \Gamma$, one has an action of $\Gamma$ on itself by $\phi$-twisted conjugacy, namely, $g.x=gx\phi(g^{-1})$. The orbits of this action are called $\phi$-twisted conjugacy classes. One says that $\Gamma$…

The classical superconformal actions of branes in adS superspaces have a closed form depending on a matrix $M^2$ quadratic in fermions, as found in hep-th/9805217. One can gauge-fix the local $\kappa$-symmetry using the Killing spinors of…

Let T be a free ergodic measure-preserving action of an abelian group G on (X,mu). The crossed product algebra R_T has two distinguished masas, the image C_T of L^infty(X,mu) and the algebra S_T generated by the image of G. We conjecture…

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…

According to Thurston's stability theorem, every group of C^1 diffeomorphisms of the closed interval is locally indicable (.e., every finitely generated subgroup factors through Z). We show that, even for finitely generated groups, the…

Assuming positive entropy we prove a measure rigidity theorem for higher rank actions on tori and solenoids by commuting automorphisms. We also apply this result to obtain a complete classification of disjointness and measurable factors for…

We show that for a large class of actions $\Gamma \curvearrowright \mathcal{A}$ of $C^*$-simple groups $\Gamma$ on unital $C^*$-algebras $\mathcal{A}$, including any non-faithful action of a hyperbolic group with trivial amenable radical,…

We prove W$^*$-superrigidity for a large class of coinduced actions. We prove that if $\Sigma$ is an amenable almost-malnormal subgroup of an infinite conjugagy class (icc) property (T) countable group $\Gamma$, the coinduced action…

We prove cocycle and orbit equivalence superrigidity for lattices in SL(n,R) acting linearly on R^n, as well as acting projectively on certain flag manifolds, including the real projective space. The proof combines operator algebraic…

Let $K$ be a compact metrizable group and $\Ga$ be a finitely generated group of commuting automorphisms of $K$. We show that ergodicity of $\Ga$ implies $\Ga$ contains ergodic automorphisms if center of the action, $Z(\Ga) = \{\ap \in {\rm…

An essentially free group action of $\Gamma$ on $(X,\mu)$ is called W*-superrigid if the crossed product von Neumann algebra $L^\infty(X) \rtimes \Gamma$ completely remembers the group $\Gamma$ and its action on $(X,\mu)$. We prove…

In this work, we promote the global $SL(2,\mathbb{R})$ symmetry of the Schwarzian derivative to a local gauge symmetry. To achieve this, we develop a procedure that potentially can be generalized beyond the $SL(2,\mathbb{R})$ case: We first…

For a locally compact abelian group $\textbf{R}$ with a uniform lattice $\Lambda$ and a group $G$ that acts on $\textbf{R}$ by continuous automorphisms, we study operators commuting with the representation of $G \rtimes \Lambda$ on…

We study 2+1 Chern-Simons gravity at the classical action level. In particular we rederive the linear combinations of the ``standard'' and ``exotic'' Einstein actions, from the (anti) self-duality of the ``internal'' Lorentzian indices. The…