Confluence on the Painlev\'e Monodromy Manifolds, their Poisson Structure and Quantisation

Marta Mazzocco; Vladimir Rubtsov

Confluence on the Painlev\'e Monodromy Manifolds, their Poisson Structure and Quantisation

Mathematical Physics 2013-01-01 v1 Algebraic Geometry Complex Variables math.MP Quantum Algebra

Authors: Marta Mazzocco , Vladimir Rubtsov

Abstract

In this paper we obtain a system of flat coordinates on the monodromy manifold of each of the Painlev\'e equations. This allows us to quantise such manifolds. We produce a quantum confluence procedure between cubics in such a way that quantisation and confluence commute. We also investigate the underlying cluster algebra structure and the relation to the versal deformations of singularities of type $D_4,A_3,A_2$ , and $A_1$ .

Keywords

moduli spaces topological quantum field theory knot invariants

Cite

@article{arxiv.1212.6723,
  title  = {Confluence on the Painlev\'e Monodromy Manifolds, their Poisson Structure and Quantisation},
  author = {Marta Mazzocco and Vladimir Rubtsov},
  journal= {arXiv preprint arXiv:1212.6723},
  year   = {2013}
}

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Version 1, 16 pages, 3 figures

Confluence on the Painlev\'e Monodromy Manifolds, their Poisson Structure and Quantisation

Abstract

Keywords

Cite

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