Skip to main content
SpringerLink
Log in

The Chekhov–Fock parametrization of Teichmüller spaces and dessins d’enfants

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

The construction of Chekhov and Fock, which associates a complex structure to a trivalent ribbon graph with real numbers on its edges, is reformulated in cartographic terms. It turns out that the “dessins d’enfants” construction corresponds to zero numbers. Two examples are discussed, and the future development of the theory is suggested.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. V. Fock and L. O. Chekhov, “Quantum mapping class group, pentagon relation, and geodesics,” Tr. Mat. Inst. Steklova, 226, 149–163 (1999).

    Google Scholar 

  2. Y. Imayoshi and M. Taniguchi, An Introduction to Teichmüller Spaces, Springer (1992).

  3. M. Kontsevich, “Intersection theory on the moduli space of curves and the matrix Airy function,” Funkts. Anal. Prilozh., 25, No. 2, 50–57 (1991).

    MathSciNet  Google Scholar 

  4. R. C. Penner, “The decorated Teichmüller space of punctured surfaces,” Commun. Math. Phys., 113, No. 2, 299–340 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  5. J.-P. Serre, Cours d’arithmétique, Presses Universitaires de France (1970).

  6. G. B. Shabat, “Complex analysis and dessins d’enfants,” in: Complex Analysis in Modern Mathematics [in Russian], Fazis, Moscow (1998), pp. 257–268.

    Google Scholar 

  7. G. B. Shabat and V. A. Voevodsky, “Drawing curves over number fields,” in: The Grothendieck Festschrift, Vol. III, Progress Math., Vol. 88, Birkhäuser (1990), pp. 199–227.

  8. P. G. Zograf and L. A. Takhtajan, “On the Liouville equation, accessory parameters, and geometry of the Teichmüller spaces of Riemann surfaces of genus zero,” Mat. Sb., 60, 143–297 (1988).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Russian State University for the Humanities, Moscow, Russia

    G. B. Shabat

  2. Deloitte, Moscow, Russia

    V. I. Zolotarskaia

Authors
  1. G. B. Shabat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Zolotarskaia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. B. Shabat.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 6, pp. 217–226, 2007.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shabat, G.B., Zolotarskaia, V.I. The Chekhov–Fock parametrization of Teichmüller spaces and dessins d’enfants. J Math Sci 158, 155–161 (2009). https://doi.org/10.1007/s10958-009-9368-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-009-9368-4

Keywords

Search

Navigation