Related papers: Poisson Principal Bundles

We introduce the description of a Wilson surface as a 2-dimensional topological quantum field theory with a 1-dimensional Hilbert space. On a closed surface, the Wilson surface theory defines a topological invariant of the principal…

In algebraic quantum field theory the spacetime manifold is replaced by a suitable base for its topology ordered under inclusion. We explain how certain topological invariants of the manifold can be computed in terms of the base poset. We…

Cohomological and Poisson structures associated with the special tautological subbundles $TB_{W_{1,2,\dots,n}}$ for the Birkhoff strata of Sato Grassmannian are considered. It is shown that the tangent bundles of $TB_{W_{1,2,\dots,n}}$ are…

This paper studies the (small) quantum homology and cohomology of fibrations $p: P\to S^2$ whose structural group is the group of Hamiltonian symplectomorphisms of the fiber $(M,\om)$. It gives a proof that the rational cohomology splits…

It is well--known that if one is given a principal $G$--bundle with a principal connection, then for every unitary finite--dimensional linear representation of $G$ one can induce a linear connection and a Hermitian structure on the…

We establish an upper bound for the cochain type level of the total space of a pull-back fibration. It explains to us why the numerical invariant for a principal bundle over the sphere are less than or equal to two. Moreover computational…

We show that unrolled quantum groups at odd roots of unity give rise to relative modular categories. These are the main building blocks for the construction of 1+1+1-TQFTs extending CGP invariants, which are non-semisimple quantum…

The dual Lie bialgebra of a certain ``quasitriangular'' Lie bialgebra structure on the Heisenberg Lie algebra determines a (non-compact) Poisson--Lie group G. The compatible Poisson bracket on G is non-linear, but it can still be realized…

We show that certain embeddable homogeneous spaces of a quantum group that do not correspond to a quantum subgroup still have the structure of quantum quotient spaces. We propose a construction of quantum fibre bundles on such spaces. The…

The BFV-formalism was introduced to handle classical systems, equipped with symmetries. It associates a differential graded Poisson algebra to any coisotropic submanifold $S$ of a Poisson manifold $(M,\Pi)$. However the assignment…

We show that principal bundles for a semisimple group on an arbitrary affine curve over an algebraically closed field are trivial, provided the order of $\pi_1$ of the group is invertible in the ground field, or if the curve has semi-normal…

We prove that the cohomology of semi-simple Lie groups admits boundary values, which are measurable cocycles on the Furstenberg boundary. This generalises known invariants such as the Maslov index on Shilov boundaries, the Euler class on…

Developing upon the ideas of ref. \ref{6}, it is shown how the theory of classical $W$ algebras can be formulated on a higher genus Riemann surface in the spirit of Krichever and Novikov. The basic geometric object is the Drinfeld--Sokolov…

We discuss the fibre bundle of co-adjoint orbits of compact Lie groups, and show how it admits a compatible K\"ahler structure. The case of the unitary group allows us to reformulate the geometric framework of quantum information theory. In…

We compute the Poisson cohomology of a class of Poisson manifolds that are symplectic away from a collection $D$ of hypersurfaces. These Poisson structures induce a generalization of symplectic and cosymplectic structures, which we call a…

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…

Quantum field theory allows more general symmetries than groups and Lie algebras. For instance quantum groups, that is Hopf algebras, have been familiar to theoretical physicists for a while now. Nowdays many examples of symmetries of…

Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…

For a compact Lie group acting on a smooth manifold, we define the differential cohomology of a certain quotient stack involving principal bundles with connection. This produces differential equivariant cohomology groups that map to the…

The Corlette-Donaldson-Hitchin-Simpson's correspondence states that, on a compact K\"ahler manifold $(X, \omega )$, there is a one-to-one correspondence between the moduli space of semisimple flat complex vector bundles and the moduli space…