Teichmüller spaces as degenerated symplectic leaves in Dubrovin–Ugaglia Poisson manifolds

  title={Teichm{\"u}ller spaces as degenerated symplectic leaves in Dubrovin–Ugaglia Poisson manifolds},
  author={Leonid Olegovich Chekhov and Marta Mazzocco},
  journal={Physica D: Nonlinear Phenomena},

Figures from this paper

Surfaces, braids, Stokes matrices, and points on spheres
Moduli spaces of points on $n$-spheres carry natural actions of braid groups. For $n=0$, $1$, and $3$, we prove that these symmetries extend to actions of mapping class groups of positive genus


Riemann surfaces with orbifold points
We interpret the previously developed Teichmüller theory of surfaces with marked points on boundary components (bordered surfaces) as the Teichmüller theory of Riemann surfaces with orbifold points
The decorated Teichmüller space of punctured surfaces
A principal ℝ+5-bundle over the usual Teichmüller space of ans times punctured surface is introduced. The bundle is mapping class group equivariant and admits an invariant foliation. Several
Teichmüller theory of bordered surfaces
We propose the graph description of Teichmuller theory of surfaces with marked points on boundary components (bordered surfaces). Introducing new parameters, we formu- late this theory in terms of
Painleve transcendents in two-dimensional topological eld theory
This paper is devoted to the theory of WDVV equations of associativity. This remarkable system of nonlinear differential equations was discovered by E. Witten [85]and R. Dijkgraaf, E. Verlinde, and
On the reductions and classical solutions of the Schlesinger equations
The Schlesinger equations S(n,m) describe monodromy preserving deformations of order m Fuchsian systems with n+1 poles. They can be considered as a family of commuting time-dependent Hamiltonian
Riemann-Hilbert problem associated to Frobenius manifold structures on Hurwitz spaces: Irregular singularity
Solutions to the Riemann-Hilbert problems with irregular singularities naturally associated to semisimple Frobenius manifold structures on Hurwitz spaces (moduli spaces of meromorphic functions on a
Monodromy of certain Painlevé–VI transcendents and reflection groups
Abstract.We study the global analytic properties of the solutions of a particular family of Painlevé VI equations with the parameters β=γ=0, δ=1/2 and 2α=(2μ-1)2 with arbitrary μ, 2μ≠∈ℤ. We introduce
We present a universal construction of almost duality for Frobenius man- ifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We
Stokes Matrices and Monodromy of the Quantum Cohomology of Projective Spaces
Abstract:In this paper we compute Stokes matrices and monodromy of the quantum cohomology of projective spaces. This problem can be formulated in a “classical” framework, as the problem of
Homotopy groups and (2 + 1)-dimensional quantum de Sitter gravity