Tr. Mat. Inst. Steklova, 2009, Volume 266, Pages 237–262
This article is cited in 7 scientific papers (total in 7 papers)
Riemann Surfaces with Orbifold Points
L. O. Chekhovabc
a Alikhanov Institute for Theoretical and Experimental Physics, Moscow, Russia
b Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
c Laboratoire J.-V. Poncelet, Moscow, Russia
We interpret the previously developed Teichmüller theory of surfaces with marked points on boundary components (bordered surfaces) as the Teichmüller theory of Riemann surfaces with orbifold points of order 2. In the Poincaré 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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Proceedings of the Steklov Institute of Mathematics, 2009, 266, 228–250
Received in February 2009
L. O. Chekhov, “Riemann Surfaces with Orbifold Points”, Geometry, topology, and mathematical physics. II, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 266, MAIK Nauka/Interperiodica, Moscow, 2009, 237–262; Proc. Steklov Inst. Math., 266 (2009), 228–250
Citation in format AMSBIB
\paper Riemann Surfaces with Orbifold Points
\inbook Geometry, topology, and mathematical physics.~II
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\publ MAIK Nauka/Interperiodica
\jour Proc. Steklov Inst. Math.
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M. Mazzocco, L. O. Chekhov, “Orbifold Riemann surfaces: Teichmüller spaces and algebras of geodesic functions”, Russian Math. Surveys, 64:6 (2009), 1079–1130
Chekhov L.O., “Orbifold Riemann surfaces and geodesic algebras”, J. Phys. A, 42:30 (2009), 304007, 32 pp.
Chekhov L., Mazzocco M., “Shear coordinate description of the quantized versal unfolding of a $D_4$ singularity”, J. Phys. A, 43:44 (2010), 442002, 13 pp.
Chekhov L., Mazzocco M., “Isomonodromic deformations and twisted Yangians arising in Teichmüller theory”, Adv. Math., 226:6 (2011), 4731–4775
Chekhov L. Mazzocco M., “Teichmüller Spaces as Degenerated Symplectic Leaves in Dubrovin-Ugaglia Poisson Manifolds”, Physica D, 241:23-24 (2012), 2109–2121
Chekhov L. Shapiro M., “Teichmüller Spaces of Riemann Surfaces with Orbifold Points of Arbitrary Order and Cluster Variables”, Int. Math. Res. Notices, 2014, no. 10, 2746–2772
Chekhov L. Mazzocco M., “Colliding Holes in Riemann Surfaces and Quantum Cluster Algebras”, Nonlinearity, 31:1 (2018), 54–107
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