Orbifold Riemann surfaces and geodesic algebras

2009/07/14 by L. O. Chekhov, L O Chekhov · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Braid group #Geodesic #Geometric and Algebraic Topology #Geometric function theory #Graph #Homotopy and Cohomology in Algebraic Topology #Orbifold #Quantum #Riemann hypothesis #Riemann surface #math-ph #math.MP #msc:53D30 #msc:81S10

paper · pdf · doi:10.1088/1751-8113/42/30/304007

published as J. Phys. A: Math. Theor. Vol.42 (2009) 304007 (32 pp.) · 39 pp., 13 figures; contribution to Memorial volume for Alesha Zamolodchikov

openalex publication_date 2009/07/14 · arxiv created 2009/11/01 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Invariants of 2+1 gravity

Cited by

• Teichmüller Spaces of Riemann Surfaces with Orbifold Points of Arbitrary Order and Cluster Variables

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