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arXiv · 1105.4501

Teichm\"uller spaces as degenerated symplectic leaves in Dubrovin--Ugaglia Poisson manifolds

Leonid Chekhov·Marta Mazzocco
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Abstract

In this paper we study the Goldman bracket between geodesic length functions both on a Riemann surface $\Sigma_{g,s,0}$ of genus $g$ with $s=1,2$ holes and on a Riemann sphere $\Sigma_{0,1,n}$ with one hole and $n$ orbifold points of order two. We show that the corresponding Teichm\"uller 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.

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Leonid Chekhov, Marta Mazzocco. 2011-05-23. Teichm\"uller spaces as degenerated symplectic leaves in Dubrovin--Ugaglia Poisson manifolds. https://doi.org/10.1016/j.physd.2011.09.018

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