相关论文: Rigidity and flexibility of group actions on the c…
We prove that rigid representations of the fundamental group of a surface into the group of oreintation-preserving homeomorphisms of the circle are geometric, thereby establishing a converse statement of a theorem by the first author.
A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and exotic smooth structures, and…
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…
Let $G$ be the group of orientation-preserving isometries of a rank-one symmetric space $X$ of non-compact type. We study local rigidity of certain actions of a solvable subgroup $\Gamma \subset G$ on the boundary of $X$, which is…
This survey aims to cover the motivation for and history of the study of local rigidity of group actions. There is a particularly detailed discussion of recent results, including outlines of some proofs. The article ends with a large number…
In this article, we describe all the group morphisms from the group of orientation-preserving homeomorphisms of the circle to the group of homeomorphisms of the annulus or of the torus.
We describe recent work that extends some of the measure and topological rigidity results in dynamical systems from situations homogeneous under a Lie group to quite general manifolds.
This book covers many of the recent results on group actions on the circle, with an emphasis in the differentiable case.
We survey some recent developments and applications of the study of the rigidity properties of natural algebraic actions of multidimensional abelian groups.
This paper has three parts. The first part is a general introduction to rigidity and to rigid actions of mapping class group actions on various spaces. In the second part, we describe in detail four rigidity results that concern actions of…
We give a criterion for the rigidity of actions on homogeneous spaces. Let $G$ be a real Lie group, $\Lambda$ a lattice in $G$, and $\Gamma$ a subgroup of the affine group Aff$(G)$ stabilizing $\Lambda$. Then the action of $\Gamma$ on…
The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation…
We prove two theorems of reduction of cocycles taking values in the group of diffeomorphisms of the circle. They generalise previous results obtained by the author concerning rigidity for smooth actions on the circle of Kazhdan's groups and…
In this article, we describe all the group morphisms from the group of compactly-supported homeomorphisms isotopic to the identity of a manifold to the group of homeomorphisms of the real line or of the circle.
Relations between parameter rigidity of locally free Lie group actions on closed manifolds and the 1st leafwise cohomology of the orbit foliations are discussed. Some computational results of the leafwise cohomology are included.
We describe our recent results concerning the rigidity/unlockability properties of clusters of rigid bodies sliding over the unit sphere.
In these lectures we consider how algebraic properties of discrete subgroups of Lie groups restrict the possible actions of those groups on surfaces. The results show a strong parallel between the possible actions of such a group on the…
We consider Abelian-by-cyclic groups for which the cyclic factor acts by hyperbolic automorphisms on the Abelian subgroup. We show that if such a group acts faithfully by $C^1$ diffeomorphisms of the closed interval with no global fixed…
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…
In this survey article, we present some panorama of groups acting on metric spaces of non-positive curvature. We introduce the main examples and their rigidity properties , we show the links between algebraic or analytic properties of the…