Related papers: Cartan decomposition of the moment map

We consider the action of a real reductive group G on a Kaehler manifold Z which is the restriction of a holomorphic action of the complexified group G^C. We assume that the induced action of a compatible maximal compact subgroup U of G^C…

Let a split element of a connected semisimple Lie group act on one of its flag manifolds. We prove that each connected set of fixed points of this action is itself a flag manifold. With this we can obtain the generalized Bruhat…

We endow the group of automorphisms of an exact Courant algebroid over a compact manifold with an infinite dimensional Lie group structure modelled on the inverse limit of Hilbert spaces (ILH). We prove a slice theorem for the action of…

In this paper we summarize some known facts on slice topology in the quaternionic case, and we deepen some of them by proving new results and discussing some examples. We then show, following [18], how this setting allows us to generalize…

Let $G$ be a Lie group acting properly on a smooth manifold $M$. If $M/G$ is connected, then we exhibit some simple and basic constructions for proper actions. In particular, we prove that the reduction principle in compact transformation…

We develop a unified approach to the classical Hopf Decomposition (also known as the conservative--dissipative decomposition) for actions of locally compact second countable groups. While the decomposition is well understood for free…

We show that the symplectic contraction map of Hilgert-Manon-Martens -- a symplectic version of Popov's horospherical contraction -- is simply the quotient of a Hamiltonian manifold $M$ by a "stratified null foliation" that is determined by…

This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment of the twisting procedure, which functorially creates new…

In this paper we introduce a new type of exponential map in semi-simple compact Lie groups, which is related to the sub-Riemannian geometry generated by the orthogonal complement of a Cartan subalgebra in a similar way to how the group…

In this paper, for a compact manifold $M$ with non-empty boundary, we give a Koiso-type decomposition theorem, as well as an Ebin-type slice theorem, for the space of all Riemannian metrics on $M$ endowed with a fixed conformal class on the…

We study hamiltonian actions of compact groups in the presence of compatible involutions. We show that the lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces…

This paper deals with the problem of finding bi-Lipschitz behavior in non-degenerate Lipschitz maps between metric measure spaces. Specifically, we study maps from (subsets of) Ahlfors regular PI spaces into sub-Riemannian Carnot groups. We…

The main result of this paper is a convexity theorem for momentum mappings of certain hamiltonian actions of noncompact semisimple Lie groups. The image is required to fall within a certain open subset D of the (dual of the) Lie algebra,…

The aim of this paper is to extend the so called slice analysis to a general case in which the codomain is a real vector space of even dimension, i.e. is of the form $\mathbb{R}^{2n}$. We define a cone $\mathcal{W}_\mathcal{C}^d$ in…

In this paper, from the viewpoint of the concentration theory of maps, we study a compact group and a L\'{e}vy group action to a large class of metric spaces, such as R-trees, doubling spaces, metric graphs, and Hadamard manifolds.

We prove a rigidity of the lightcone in Minkowski space. It is essentially the unique space endowed with a degenerate Riemannian metric, of lightlike type, and supporting an isometric non-proper action of a semi-simple group.

We give a complete characterization of Hamiltonian actions of compact Lie groups on exact symplectic manifolds with proper momentum maps. We deduce that every Hamiltonian action of a compact Lie group on a contractible symplectic manifold…

We show that the main theorem of Morse theory holds for a large class of functions on singular spaces. The function must satisfy certain conditions extending the usual requirements on a manifold that Condition C holds and the gradient flow…

In this paper we use some basic facts from the theory of (matrix) Lie groups and algebras to show that many of the classical matrix splittings used to construct stationary iterative methods and preconditioniers for Krylov subspace methods…

We study the sub-Riemannian structure determined by a left-invariant distribution of rank 2 on a step 3 Carnot group of dimension 5. We prove the conjectured cut times of Y. Sachkov for the sub-Riemannian Cartan problem. Along the proof, we…