Related papers: WZW-Poisson manifolds

Given an oriented surface S with base point * on the boundary, we introduce for all N>0, a canonical quasi-Poisson bracket on the space of N-dimensional linear representations of \pi_1(S,*). Our bracket extends the well-known Poisson…

We propose a geometrical interpretation for the discrete torsion appearing in the algebraic formulation of quotients of WZW models by discrete abelian subgroups. Part of the discrete torsion corresponds to the choice of action of the…

We introduce the notion of a manifold admitting a simple compact Cartan 3-form $\om^3$. We study algebraic types of such manifolds specializing on those having skew-symmetric torsion, or those associated with a closed or coclosed 3-form…

We construct a class of topological field theories with Wess-Zumino term in spacetime dimensions $\ge 2$ whose target space has a geometrical structure that suitably generalizes Poisson or twisted Poisson manifolds. Assuming a field content…

Given a closed, oriented Lagrangian submanifold $L$ in a Liouville domain $\overline{M}$, one can define a Maurer-Cartan element with respect to a certain $L_\infty$-structure on the string homology…

In this letter, first we give a decomposition for any Lie-Poisson structure $\pi_g$ associated to the modular vector. In particular, $\pi_g$ splits into two compatible Lie-Poisson structures if $dim{g} \leq 3$. As an application, we…

We analyze unoriented Wess-Zumino-Witten models from a geometrical point of view. We show that the geometric interpretation of simple current crosscap states is as centre orientifold planes localized on conjugacy classes of the group…

A Koszul-Vinberg manifold is a manifold $M$ endowed with a pair $(\nabla,h)$ where $\nabla$ is a flat connection and $h$ is a symmetric bivector field satisfying a generalized Codazzi equation. The geometry of such manifolds could be seen…

The values of the Witten invariants, $I_W$, of the lens space $L(p, 1)$ for SU(2) at level $k$ are obtained for arbitrary $p$. A duality relation for $I_W$ when $p$ and $k$ are interchanged, valid for asymptotic $k$, is observed. A method…

We define Poisson structures on certain transversal slices to conjugacy classes in complex simple algebraic groups introduced in arXiv:0809.0205. These slices are associated to the elements of the Weyl group, and the Poisson structures on…

Let R be a commutative ring, and let A be a Poisson algebra over R. We construct an (R,A)-Lie algebra structure, in the sense of Rinehart, on the A-module of K\"ahler differentials of A depending naturally on A and the Poisson bracket. This…

Given a foliation S of a manifold M, a distribution Z in M transveral to S and a Poisson bivector \Pi on M we present a geometric method of reducing this operator on the foliation S along the distribution Z. It encompasses the classical…

We describe a deformation quantization of a modification of Poisson geometry by a closed 3-form. Under suitable conditions it gives rise to a stack of algebras. The basic object used for this aim is a kind of families of Poisson structures…

Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by…

We develop the theory of Poisson and Dirac manifolds of compact types, a broad generalization in Poisson and Dirac geometry of compact Lie algebras and Lie groups. We establish key structural results, including local normal forms, canonical…

We give a criterion on a group $\pi$ and a homomorphism $w \colon \pi \to C_2$ under which closed $4$-manifolds with fundamental group $\pi$ and orientation character $w$ are classified up to homotopy equivalence by their quadratic…

The semi-classical data attached to stacks of algebroids in the sense of Kashiwara and Kontsevich are Maurer-Cartan elements on complex manifolds, which we call extended Poisson structures as they generalize holomorphic Poisson structures.…

The correspondence between Poisson structures and symplectic groupoids, analogous to the one of Lie algebras and Lie groups, plays an important role in Poisson geometry; it offers, in particular, a unifying framework for the study of…

Given an $L^2$-acyclic connected finite $CW$-complex, we define its universal $L^2$-torsion in terms of the chain complex of its universal covering. It takes values in the weak Whitehead group $\operatorname{Wh}^w(G)$. We study its main…

A $2n$-dimensional Poisson manifold $(M ,\Pi)$ is said to be $b^m$-symplectic if it is symplectic on the complement of a hypersurface $Z$ and has a simple Darboux canonical form at points of $Z$ which we will describe below. In this paper…