Related papers: Some remarks on polar actions

We construct harmonic Riemannian submersions that are retractions from symmetric spaces of noncompact type onto their rank-one totally geodesic subspaces. Among the consequences, we prove the existence of a non-constant, globally defined…

We prove that a polar orthogonal representation of a real reductive algebraic group has the same closed orbits as the isotropy representation of a pseudo-Riemannian symmetric space. We also develop a partial structural theory of polar…

We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.

The author proposes a method for investigating actions of finite groups on aspherical spaces. Complete homotopy classification of free actions of finite groups on aspherical spaces is obtained. Also there are some results about non-free…

Let the compact torus $T^{n-1}$ act on a smooth compact manifold $X^{2n}$ effectively with nonempty finite set of fixed points. We pose the question: what can be said about the orbit space $X^{2n}/T^{n-1}$ if the action is cohomologically…

We show that the inverse limit and the orbit map commute for actions of compact groups on compact Hausdorff spaces.

A polar space S is said to be symplectic if it admits an embedding e in a projective geometry PG(V) such that the e-image e(S) of S is defined by an alternating form of V. In this paper we characterize symplectic polar spaces in terms of…

The (local) invariant symplectic action functional $\A$ is associated to a Hamiltonian action of a compact connected Lie group $\G$ on a symplectic manifold $(M,\omega)$, endowed with a $\G$-invariant Riemannian metric $<\cdot,\cdot>_M$. It…

It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. We answer this question…

We study polar representations in the sense of Dadok and Kac which are symplectic. We show that such representations are coisotropic and use this fact to give a classification. We also study their moment maps and prove that they separate…

By a Cantor group we mean a topological group homeomorphic to the Cantor set. The author earlier proved that every compact metric space of rational cohomological dimension n can be obtained as the orbit space of a Cantor group action on a…

Let $G$ be a connected Lie group of rank one. In this paper the existence of free actions of group $G$ on spheres, real projective spaces and lens spaces has been studied. Most of the results have been obtained for finitistic spaces with…

We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…

We obtain a partial converse of Vershik's description of ergodic probability measures on a compact metric space with respect to an isometric action by an inductively compact group. This allows us to identify, in this setting, the set of…

We prove a compactness result for classes of actions of many small categories on quantum compact metric spaces by Lipschitz linear maps, for the topology of the covariant Gromov-Hausdorff propinquity. In particular, our result applies to…

We prove results about orbit closures and equidistribution for the SL(2,R) action on the moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent flows. The proofs of the main theorems rely on the measure…

We prove the rigidity of presymplectic actions of a compact semisimple Lie algebra on a presymplectic manifold of constant rank in the local and global case. The proof uses an abstract normal form theorem we had stated in a previous work,…

We discuss properties of orbits of (semi)group actions on locally compact groups G. In particular, we show that if a compactly generated locally compact abelian group acts distally on G then the closure of each of its orbits is a minimal…

We define and study Poissonian actions of Polish groups as a framework to Poisson suspensions, characterize them spectrally, and provide a complete characterization of their ergodicity. We further construct 'spatial' Poissonian actions,…

We generalise results about isometric group actions on metric spaces and their fundamental regions to the context of merely continuous group actions. In particular, we obtain results that yield the relative compactness of a fundamental…