Abstract
In this paper, we study the Goldman bracket between geodesic length functions both on a Riemann surface Σg,s,0 of genus g with s=1,2 holes and on a Riemann sphere Σ0,1,n with one hole and n orbifold points of order two. We show that the corresponding Teichmüller spaces Tg,s,0 and T0,1,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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