Related papers: An obstruction to the local lifting problem

We prove a true bootstrapping result for convergence groups acting on a Peano continuum. We give an example of a Kleinian group H which is the amalgamation of two closed hyperbolic surface groups along a simple closed curve. The limit set…

We obtain restrictions on units of even order in the integral group ring $\mathbb{Z}G$ of a finite group $G$ by studying their actions on the reductions modulo $4$ of lattices over the $2$-adic group ring $\mathbb{Z}_2G$. This improves the…

Consider a Hamiltonian action by biholomorphisms of a compact Lie group $K$ on a Kaehler manifold $X$, with moment map $\mu:X\to\klie^*$. We characterize which orbits of the complexified action of $G=K^{\CC}$ in $X$ intersect $\mu^{-1}(0)$…

We show that most homogeneous Anosov actions of higher rank Abelian groups are locally smoothly rigid (up to an automorphism). This result is the main part in the proof of local smooth rigidity for two very different types of algebraic…

We prove a compactness result with respect to $\Gamma$-convergence for a class of integral functionals which are expressed as a sum of a local and a non-local term. The main feature is that, under our hypotheses, the local part of the…

Given a partial action of a topological group $G$ on a space $X$, we determine properties $\mathcal P$ which can be extended from $X$ to its globalization. We treat the cases when $\mathcal P$ is any of the following: Hausdorff, regular,…

For a smooth projective variety $X$ defined over a global field $K$, one can form a notion of Weak Approximation for the Chow group of zero-cycles of $X$. There exists a Brauer-Manin obstruction to Weak Approximation here akin to that for…

Let $p$ be a prime and $F$ a non-archimedean local field of residue characteristic $p$. In this paper, we study the restriction of smooth irreducible $\bar{\mathbb{F}}_p$-representations of $\mathrm{SL}_2(F)$ to its Borel subgroup. In…

Let L be a reductive subgroup of a reductive Lie group G. Let G/H be a homogeneous space of reductive type. We provide a necessary condition for the properness of the action of L on G/H. As an application we give examples of spaces that do…

It is well-known that an effective orbifold M (one for which the local stabilizer groups act effectively) can be presented as a quotient of a smooth manifold P by a locally free action of a compact lie group K. We use the language of…

We study locally compact convergence groups, in particular the link between the convergence property and the Specker compactifications (a genaralization of the ends) of a group.

Finite non-abelian non-metacyclic $2$-generated $p$-groups (${p>2}$) of nilpotency class $2$ with cyclic commutator subgroup which are the additive groups of local nearrings are described. It is shown that the subgroup of all non-invertible…

We consider the following problem. Suppose $\alpha$ is an action of a locally compact group $G$ on a $C^*$-algebra $A$, $H$ is a closed subgroup of $G$, and $(\pi,U)$ is a covariant representation of $(A,H,\alpha)$. For which closed…

We prove that arithmetic quantum unique ergodicity holds on compact arithmetic quotients of $GL(2,\mathbb{Q}_p)$ for automorphic forms belonging to the principal series. We interpret this conclusion in terms of the equidistribution of…

In this paper we find all solvable subgroups of Diff^omega(S^1) and classify their actions. We also investigate the C^r local rigidity of actions of the solvable Baumslag-Solitar groups on the circle. The investigation leads to two novel…

We establish a necessary and sufficient condition for an action of a lattice by homeomorphisms of the circle to extend continuously to the ambient locally compact group. This condition is expressed in terms of the real bounded Euler class…

Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by the gluing equations for PGL(3,C)-representations. In…

Our aim in this paper is to study local rigidity for metrics defined on a compact manifold $M$ with boundary satisfying constant scalar curvature on $M$ and constant mean curvature on $\partial M$. We present some geometrical hypotheses…

A locally compact group $G$ is said to have shifted convolution property (abbr. as SCP) if for every regular Borel probability measure $\mu$ on $G$, either $\sup_{x\in G} \mu ^n (Cx) \ra 0$ for all compact subsets $C$ of $G$, or there exist…

This paper deals with the periodic homogenization of nonlocal parabolic Hamilton-Jacobi equations with superlinear growth in the gradient terms. We show that the problem presents different features depending on the order of the nonlocal…