Related papers: Sur Les Actions Symplectiques Quasi-Primitives

Let $G$ be a complex semisimple algebraic group and $X$ be a complex symmetric homogeneous $G$-variety. Assume that both $G$, $X$ as well as the $G$-action on $X$ are defined over real numbers. Then $G(\mathbb{R})$ acts on $X(\mathbb{R})$…

We show that generic symplectic quotients of a Hamiltonian $G$-space $M$ by the action of a compact connected Lie group $G$ are also symplectic quotients of the same manifold $M$ by a compact torus. The torus action in question arises from…

In this paper we continue the study of groups of trace class and consider in particular the case of semi-direct products. One of the highlights is the theorem saying that the semi-direct product of a semisimple Lie group G and its Lie…

Let $G$ be a compact and connected Lie group. The Hamiltonian $G$-model functor maps the category of symplectic representations of closed subgroups of $G$ to the category of exact Hamiltonian $G$-actions. Based on previous joint work with…

Symmetric symplectic spaces of Ricci type are a class of symmetric symplectic spaces which can be entirely described by reduction of certain quadratic Hamiltonian systems in a symplectic vector space. We determine, in a large number of…

For finitely generated groups $G$ and $H$ equipped with word metrics, a translation-like action of $H$ on $G$ is a free action where each element of $H$ moves elements of $G$ a bounded distance. Translation-like actions provide a geometric…

Let X be a smooth projective variety of dimension n on which a simple Lie group G acts regularly and non trivially. Then X is not minimal in the sense of the Minimal Model Program. In the paper we work out a classification of X via the…

In this note we prove that an analytic symplectic action of a semisimple Lie algebra can be locally linearized in Darboux coordinates. This result yields simultaneous analytic linearization for Hamiltonian vector fields in a neighbourhood…

We introduce the process of symplectic reduction along a submanifold as a uniform approach to taking quotients in symplectic geometry. This construction holds in the categories of smooth manifolds, complex analytic spaces, and complex…

Topologically and geometrically engaging actions have proved to be useful to obtain rigidity results for semisimple Lie group actions. We show that the action of a simple noncompact Lie group on a compact manifold preserving a unimodular…

Let G be a connected semisimple Lie group without compact factors whose real rank is at least 2, and let \Gamma \subset G be an irreducible lattice. We provide a C^\infty classification for volume-preserving Cartan actions of \Gamma and G.…

We construct a 6-manifold M which admits a smooth circle action and a symplectic form w such that if w' is another symplectic form on M equivalent to w, then (M,w') does not admit a symplectic circle action.

For a finite dimensional Lie algebra $\g$ of vector fields on a manifold $M$ we show that $M$ can be completed to a $G$-space in a unversal way, which however is neither Hausdorff nor $T_1$ in general. Here $G$ is a connected Lie group with…

Suppose that $\tilde{G}$ is a connected reductive group defined over a field $k$, and $\Gamma$ is a finite group acting via $k$-automorphisms of $\tilde{G}$ satisfying a certain quasi-semisimplicity condition. Then the connected part of the…

We prove that a group $\Gamma$ admits a discrete topological (equivalently, smooth) action on some simply-connected 3-manifold if and only if $\Gamma$ has a Cayley complex embeddable -- with certain natural restrictions -- in one of the…

The aim of this paper is characterizing right subdirectly irreducible completely 0-simple semigroups. We prove that such semigroups are indeed groups with least nontrivial subgroups. On the other hand we prove that right irreducible…

Zimmer's superrigidity theorems on higher rank Lie groups and their lattices launched a program of study aiming to classify actions of semisimple Lie groups and their lattices, known as the {\it Zimmer program}. When the group is too large…

We give a systematic treatment of the stability theory for action of a real reductive Lie group G on a topological space. More precisely, we introduce an abstract setting for actions of non-compact real reductive Lie groups on topological…

The coadjoint representation of a connected algebraic group $Q$ with Lie algebra $\mathfrak q$ is a thrilling and fascinating object. Symmetric invariants of $\mathfrak q$ (= $\mathfrak q$-invariants in the symmetric algebra $S(\mathfrak…

Let $G$ be a countable group and $X$ be a totally regular curve. Suppose that $\phi:G\rightarrow {\rm Homeo}(X)$ is a minimal action. Then we show an alternative: either the action is topologically conjugate to isometries on the circle…