Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, Epiciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Painlevé monodromy manifolds, decorated character varieties and cluster algebras

Abstract :

In this paper we introduce the concept of decorated character variety for the Riemann surfaces arising in the theory of the Painlevé differential equations. Since all Painlevé differential equations (apart from the sixth one) exhibit Stokes phenomenon, it is natural to consider Riemann spheres with holes and bordered cusps on such holes. The decorated character is defined as complexification of the bordered cusped Teichm ̈uller spaceintroduced in [8]. We show that the decorated character variety of a Riemann sphere withs holes and n >1 cusps is a Poisson manifold of dimension 3s+ 2n−6 and we explicitly compute the Poisson brackets which are naturally of cluster type. We also show how to obtain the confluence procedure of the Painlevé differential equations in geometric terms.

Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [25 references]  Display  Hide  Download
Contributor : Okina Univ Angers Connect in order to contact the contributor
Submitted on : Wednesday, November 18, 2015 - 2:31:18 PM
Last modification on : Wednesday, October 20, 2021 - 3:18:54 AM
Long-term archiving on: : Friday, February 19, 2016 - 10:33:21 AM


Files produced by the author(s)


  • HAL Id : hal-01228533, version 1
  • OKINA : ua14192



Leonid Chekhov, Marta Mazzocco, Vladimir Roubtsov. Painlevé monodromy manifolds, decorated character varieties and cluster algebras. 2015. ⟨hal-01228533⟩



Record views


Files downloads