Related papers: Wild genus-zero quantum de Rham spaces

Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…

Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…

We present a spectral sequence for free isometric Lie algebra actions (and consequently locally free isometric Lie group actions) which relates the de Rham cohomology of the manifold with the Lie algebra cohomology and basic cohomology…

Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…

Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the \Teich parameters, parameterizing the purely global geometry. One of the key…

A homogeneous Riemannian manifold $(M=G/K, g)$ is called a space with homogeneous geodesics or a $G$-g.o. space if every geodesic $\gamma (t)$ of $M$ is an orbit of a one-parameter subgroup of $G$, that is $\gamma(t) = \exp(tX)\cdot o$, for…

Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the…

We show there exists a rigid monoidal category formed out by quantum linear spaces with an additional structure, such that FRT bialgebras and corresponding rectangular generalizations are its internal coEnd and coHom objects, respectively.…

We study pseudoholomorphic curves in symplectic quotients as adiabatic limits of solutions of a system of nonlinear first order elliptic partial differential equations in the ambient symplectic manifold. The symplectic manifold carries a…

Let X=G/K be a connected Riemannian homogeneous space of a real Lie group G. The homogeneous space X is called commutative if the algebra of G-invariant differential operators on X is commutative. We prove an effective commutativity…

We construct smooth bundles with base and fiber products of two spheres whose total spaces have non-vanishing $\hat{A}$-genus. We then use these bundles to locate non-trivial rational homotopy groups of spaces of Riemannian metrics with…

If K is a commutative ring and A is a K-algebra, for any sequence $\sigma $ of positive integers there exists an higher order analogue dR($\sigma $) of the standard de Rham complex dR(1,...,1,...), which can also be defined starting from…

It is explained how to find the de~Rham decomposition of a Riemannian manifold and the Wu decomposition of a Lorentzian manifold. For that it is enough to find parallel symmetric bilinear forms on the manifold, and do some linear algebra.…

In this expository paper, we give a complete proof of van den Essen's theorem that the de Rham cohomology spaces of a holonomic D-module are finite-dimensional in the case of a formal power series ring over a field of characteristic zero.…

Let $V$ be a quasi-conformal grading-restricted vertex algebra, $W$ be its module, and $\W_{z_1, \ldots, z_n}$ be the space of rational differential forms with complex parameters $(z_1, \ldots, z_n)$ for $n \ge 0$. Using geometric…

In this paper we study general hyperplane sections of adjoint and coadjoint varieties. We show that these are the only sections of homogeneous varieties such that a maximal torus of the automorphism group of the ambient variety stabilizes…

Let $M$ be complete flat pseudo-Riemannian homogeneous manifold and $\Gamma\subset\Iso(\RR^n_s)$ its fundamental group. We show that $M$ is a trivial fiber bundle $G/\Gamma\to M\to\RR^{n-k}$, where $G$ is the Zariski closure of $\Gamma$ in…

Let X be a compact connected Riemann surface of genus at least two. Let r be a prime number and \xi a holomorphic line bundle on it such that r is not a divisor of degree(\xi). Let {\mathcal M}_\xi(r) denote the moduli space of stable…

We study several integrable Hamiltonian systems on the moduli spaces of meromorphic functions on Riemann surfaces (the Riemann sphere, a cylinder and a torus). The action-angle variables and the separated variables (in Sklyanin's sense) are…

In this paper we develop fundamental tools and methods to study meromorphic functions in an equivariant setup. As our main result we construct quotients of Rosenlicht-type for Stein spaces acted upon holomorphically by complex-reductive Lie…