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A quantum Teichmüller space

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Abstract

We explicitly describe a noncommutative deformation of the *-algebra of functions on the Teichmüller space of Riemann surfaces with holes that is equivariant with respect to the action of the mapping class group.

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References

  1. H. Verlinde and E. Verlinde, “Conformal field theory and geometric quantization,” in:Superstrings 1989 (Trieste, 1989) (M. Green et al., eds.), World Scientific, River Edge, NJ (1990), pp. 422–449.

    Google Scholar 

  2. E. Witten, “The central charge in three dimensions,” in:Physics and Mathematics of Strings (L. Brink, D. Friedan and A. M. Polyakov, eds.), World Scientific, Teaneck, NJ (1990), pp. 530–559.

    Google Scholar 

  3. S. Carlip,Quantum Gravity in 2+1 Dimensions, Cambridge Univ. Press, Cambridge (1998).

    MATH  Google Scholar 

  4. L. D. Faddeev and R. M. Kashaev,Mod. Phys. Lett. A,9, 427–434 (1994); “Quantum dilogarithm,” Preprint hep-th/9310070 (1993).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. R. M. Kashaev,Lett. Math. Phys.,43, No. 2, 105–115 (1998); “Quantization of Teichmüller spaces and the quantum dilogarithm,” Preprint q-alg/9706018 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  6. O. Ya. Viro, “Lectures on combinatorial presentations of manifolds,” in:Differential Geometry and Topology (Alghero, 1992) (R. Caddeo and F. Tricerri, eds.), World Scientific, River Edge, NJ (1993), pp. 244–264.

    Google Scholar 

  7. K. Strebel,Quadratic Differentials, Springer, Berlin (1984).

    MATH  Google Scholar 

  8. R. C. Penner,Commun. Math. Phys.,113, 299 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  9. V. V. Fock, “Dual Teichmüller spaces,” Preprint, MPIM, Bonn (1997); Preprint hep-th/9702018 (1997).

    Google Scholar 

  10. W. M. Goldman,Adv. Math.,54, 200–225 (1984).

    Article  MATH  Google Scholar 

  11. G. Lion and M. Vergne,The Weil Representation, Maslov Index, and Theta Series (Progress in Mathematics, Vol. 6), Birkhäuser, Boston, Mass. (1980).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute for Theoretical and Experimental Physics, Moscow, Russia

    V. V. Fock

  2. Steklov Mathematical Institute, RAS, Moscow, Russia

    L. O. Chekhov

Authors
  1. V. V. Fock
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  2. L. O. Chekhov
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Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 120, No. 3, pp. 511–528, September, 1999.

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Fock, V.V., Chekhov, L.O. A quantum Teichmüller space. Theor Math Phys 120, 1245–1259 (1999). https://doi.org/10.1007/BF02557246

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  • DOI: https://doi.org/10.1007/BF02557246

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