Abstract
We interpret the previously developed Teichmuller theory of surfaces with marked points on boundary components (bordered surfaces) as the Teichmuller theory of Riemann surfaces with orbifold points of order 2. In the Poincare uniformization pattern, we describe necessary and sufficient conditions for the group generated by the Fuchsian group of the surface with added inversions to be of the almost hyperbolic Fuchsian type. All the techniques elaborated for the bordered surfaces (quantization, classical and quantum mapping-class group transformations, and Poisson and quantum algebra of geodesic functions) are equally applicable to the surfaces with orbifold points.
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