Teichmuller spaces of orbifold Riemann surfaces and geodesic algebras

Abstract:

We generalize the Penner--Fock fat graph technique to the case of Riemann surfaces with Z_2-orbifold points. The corresponding Poisson algebras of geodesic functions are of A_n (Nelson-Regge-Ugaglia-Bondal) type for the Poincare disc with n orbifold points and of a new, D_n type for the annulus with n orbifold points.

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