相关论文: Analysis and geometry on marked configuration spac…

In this paper, we compute the Gerstenhaber bracket on the Hoch-schild cohomology of $C^\infty(M)\rtimes G$ for a finite group $G$ acting on a compact manifold $M$. Using this computation, we obtain geometric descriptions for all…

The space $\Gamma_X$ of all locally finite configurations in a Riemannian manifold $X$ of infinite volume is considered. The deRham complex of square-integrable differential forms over $\Gamma_X$, equipped with the Poisson measure, and the…

Let $X$ be a manifold with a bi-Poisson structure $\{\eta^t\}$ generated by a pair of $G$-invariant symplectic structures $\omega_1$ and $\omega_2$, where the Lie group $G$ acts properly on $X$. Let $H$ be some isotropy subgroup for this…

Swarm and constellation reconfiguration can be viewed as motion of an unordered point configuration in an ambient space. Here, we provide persistence-stable, symmetry-invariant geometric representations for comparing and monitoring…

In this paper we put together some tools from differential topology and analysis in order to study second order semi-linear partial differential equations on a Riemannian manifold $M$. We look for solutions that are constants along orbits…

This paper develops new aspects of the interplay between shifted symplectic geometry and classical Poisson geometry, focusing on lagrangian morphisms into 2-shifted symplectic groups. We establish a Lie-type correspondence between such…

We introduce the concept of partial Poisson structure on a manifold $M$ modelled on a convenient space. This is done by specifying a (weak) subbundle $T^{\prime}M$ of $T^{\ast}M$ and an antisymmetric morphism $P:T^{\prime}M\rightarrow TM$…

For an element $\Psi$ in the graded vector space $\Omega^*(M, TM)$ of tangent bundle valued forms on a smooth manifold $M$, a $\Psi$-submanifold is defined as a submanifold $N$ of $M$ such that $\Psi_{|N} \in \Omega^*(N, TN)$. The class of…

We study a formulation of the standard Poisson sigma model in which the target space Poisson manifold carries the Hamilton action of some finite dimensional Lie algebra. We show that the structure of the action and the properties of the…

We give simple explicit formulas for deformation quantization of Poisson-Lie groups and of similar Poisson manifolds which can be represented as moduli spaces of flat connections on surfaces. The star products depend on a choice of…

Let $\Gamma_X$ denote the space of all locally finite configurations in a complete, stochastically complete, connected, oriented Riemannian manifold $X$, whose volume measure $m$ is infinite. In this paper, we construct and study spaces…

We study Dirac structures associated with Manin pairs (\d,\g) and give a Dirac geometric approach to Hamiltonian spaces with D/G-valued moment maps, originally introduced by Alekseev and Kosmann-Schwarzbach in terms of quasi-Poisson…

Let X be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X, and let \g denote the complexification of the Lie algebra of U, \g=\u^\C. Each…

In this paper we consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We realize the dual space Y^h(M) of the Hardy-type space X^h(M), introduced in a previous paper of the authors, as the…

Let $\Omega=G/K$ be a bounded symmetric domain and $S=K/L$ its Shilov boundary. We consider the action of $G$ on sections of a homogeneous line bundle over $\Omega$ and the corresponding eigenspaces of $G$-invariant differential operators.…

We develop a set of sufficient conditions for guaranteeing that an integrable system with a symmetry group $K$ on a manifold $M$ descends to an integrable system on a dense open subset of the quotient Poisson space $M/K$. The higher…

Let $M^{2n}$ be a Poisson manifold with Poisson bivector field $\Pi$. We say that $M$ is b-Poisson if the map $\Pi^n:M\to\Lambda^{2n}(TM)$ intersects the zero section transversally on a codimension one submanifold $Z\subset M$. This paper…

In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure (\cite{Nas2}) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson…

We consider the following construction of quantization. For a Riemannian manifold $M$ the space of forms on $T^*M$ is made into a space of (full) symbols of operators acting on forms on $M$. This gives rise to the composition of symbols,…

This paper contributes to foundations of the geometric measure theory in the infinite dimensional setting of the configuration space over the Euclidean space $\mathbb R^n$ equipped with the Poisson measure $\pi$. We first provide a rigorous…