Teichmüller spaces as degenerated symplectic leaves in Dubrovin–Ugaglia Poisson manifolds
Copyright policy )Teichmüller spaces as degenerated symplectic leaves in Dubrovin–Ugaglia Poisson manifolds
In this paper we study the Goldman bracket between geodesic length functions both on a Riemann surface $Σ_{g,s,0}$ of genus $g$ with $s=1,2$ holes and on a Riemann sphere $Σ_{0,1,n}$ with one hole and $n$ orbifold points of order two. We show that the corresponding Teichmüller spaces $\mathcal T_{g,s,0}$ and $\mathcal T_{0,1,n}$ are realised as real slices of degenerated symplectic leaves in the Dubrovin--Ugaglia Poisson algebra of upper--triangular matrices $S$ with 1 on the diagonal.
27 pages, 7 figures, contribution to special issue of Physica D on Boris Dubrovin 60th birthday
- Loughborough University United Kingdom
- Steklov Mathematical Institute Russian Federation
- Department of Mathematical Sciences Russian Federation
High Energy Physics - Theory, Teichmüller space, FOS: Physical sciences, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Goldman bracket, Condensed Matter Physics, Monodromy preserving deformations, High Energy Physics - Theory (hep-th), monodromy preserving deformations, Compact Riemann surfaces and uniformization, Teichmüller theory for Riemann surfaces, Stokes matrix, Mathematical Physics
High Energy Physics - Theory, Teichmüller space, FOS: Physical sciences, Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Goldman bracket, Condensed Matter Physics, Monodromy preserving deformations, High Energy Physics - Theory (hep-th), monodromy preserving deformations, Compact Riemann surfaces and uniformization, Teichmüller theory for Riemann surfaces, Stokes matrix, Mathematical Physics
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