Skip to main content

[96] On E. Verlinde’s Formula in the Context of Stable Bundles

  • Chapter
  • First Online:
Raoul Bott: Collected Papers

Part of the book series: Contemporary Mathematicians ((CM))

  • 1362 Accesses

Abstract

E. Verlinde’s formula for the dimension of the nonabelian θ-functions is discussed from an algebraic geometry point of view and related to certain quotient rings of the representative ring of sums.

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

Access this chapter

Institutional subscriptions

Bibliography

  • M.F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc., London A 308 (1982), 523-615.

    Article  MathSciNet  Google Scholar 

  • S. Axelrod, S. Della Pietra, and E. Witten, Geometrie quantization of Chern Simons gauge theory, IAS Preprint, Oct. 1989.

    Google Scholar 

  • A. Beauville, M.S. Narasimhan, and S. Ramanan, Spectral curves and the generalized theta divisor, J. reine angew. Math. 398 (1989), 169-179.

    MathSciNet  MATH  Google Scholar 

  • G.D. Daskalopoulos, The topology of the space of stable bundles on a compact riemann surface I, to be published.

    Google Scholar 

  • J.-M. Drezet and M.S. Narasimhan, Groupe de Picard des variétés de modules de fìbrés sem-stables sur les courbes algébriques, Invent. Math. 97 (1989), 53-94.

    Article  MathSciNet  Google Scholar 

  • N.J. Hitchin, Fiat Connections and Geometrie Quantization, Preprint, Jan., 1990.

    Google Scholar 

  • G. Harder, Eine Bemerkung zu einer Arbeit von P.E. Newstead, J. Math. 242 (1970), 16-25.

    MathSciNet  MATH  Google Scholar 

  • G. Harder and M.S. Narasimhan, On the cohomology groups of moduli spaces of vector bundles over curves, Math. Annalen 212, (1975), 215-248.

    Article  Google Scholar 

  • D. Mumford, Geometric invariant theory, Ergebnisse der Mathematik, Springer (Berlin- Heidelberg-New York), 1965.

    Google Scholar 

  • V.B. Mehta and C.S. Seshadri, Moduli of vector bundles on curves with parabolic structures, Math. Ann. 248. 205-239 (1980).

    Article  MathSciNet  Google Scholar 

  • P.E. Newstead, Topological properties of some spaces of stable bundles, Topology, Pergamon Press, vol. 6 (1967), 241-262.

    Article  MathSciNet  Google Scholar 

  • Oxford Seminar on Jones-Witten Theory, Michaelmas Term 1988.

    Google Scholar 

  • T.R. Ramadas, Chern-Simons gauge theory and projectively flat vector bundles on Mg y MIT Preprint, 1989.

    Google Scholar 

  • C.S. Seshadri, Space of unitary vector bundles on a compact Riemann surface, Ann. of Math. M (1967), 303-336.

    Article  MathSciNet  Google Scholar 

  • S.S. Shatz, The decomposition and specialization of algebraic families of vector bun¬dles, Compositio Math.35 (1977), 163-187.

    MathSciNet  MATH  Google Scholar 

  • M. Thaddeus, Conformai field theory and the cohomology of the moduli space of stable bundles, Math. Inst., Oxford, England, in preparation.

    Google Scholar 

  • T. Tsuchiya, K. Ueno, and T. Yamada, Conf. F., Theory on universal family of stable curves with gauge symmetries, Advanced Studies in Pure Math. 19 (1989), 459-565.

    Google Scholar 

  • H. Veriinde and E. Veriinde, Conformai field theory and geometric quantization, IAS Preprint, Oct. 1989.

    Google Scholar 

  • E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 (1989), 351-399.

    Article  MathSciNet  Google Scholar 

  • E. Witten, Topological quantum field theory, Commun. Math. Phys. 117 (1988), 353-386.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bott, R. (2017). [96] On E. Verlinde’s Formula in the Context of Stable Bundles. In: Tu, L. (eds) Raoul Bott: Collected Papers . Contemporary Mathematicians. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-51781-0_20

Download citation

Publish with us

Policies and ethics