Orbifold Riemann surfaces and geodesic algebras

Details Orbifold Riemann surfaces and geodesic algebras Orbifold Riemann surfaces and geodesic algebras

2009-11-01

arxiv.org/abs/0911.0214v1

J. Phys. A: Math. Theor. Vol.42 (2009) 304007 (32 pp.)

Physics

Mathematical Physics

39 pp., 13 figures; contribution to Memorial volume for Alesha Zamolodchikov

Scientific paper

We study the Teichm\"uller theory of Riemann surfaces with orbifold points of order two using the fat graph technique. The previously developed technique of quantization, classical and quantum mapping-class group transformations, and Poisson and quantum algebras of geodesic functions is applicable to the surfaces with orbifold points. We describe classical and quantum braid group relations for particular sets of geodesic functions corresponding to $A_n$ and $D_n$ algebras and describe their central elements for the Poisson and quantum algebras.

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