Morse Theoretic Aspects of Yang-Mills Theory

  • Raoul Bott
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 59)


Let me start in the manner I have learned of late from all you Physicists, with a modest list of topics to be covered in these two lectures. My topics are:
  1. (i)

    Algebraic topology

  2. (ii)

    Morse theory

  3. (iii)

    Equivariant Morse theory

  4. (iv)

    Pertinence of (i), (ii), and (iii) to the solutions of the classical Yang-Mills Equations.



Modulus Space Vector Bundle Riemann Surface Conjugate Point Morse Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Bott and H. Samelson, Applications of the theory of Morse to symmetric spaces, Amer. J. of Math. vol. 80 (1968), pp. 964–1029.MathSciNetCrossRefGoogle Scholar
  2. 2.
    G. Harder, Eine Bemerkung Zu einer Arbeit von P. E. Newstead, Jour. fur Math. 242 (1970), 16–25.MathSciNetMATHGoogle Scholar
  3. 3.
    G. Harder and M. S. Narasimhan, On the cohomology groups of moduli spaces of vector bundles over curves, Math. Ann. 212 (1975), 215–248.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    D. Mumford and P. E. Newstead, Periods of a moduli space of bundles on curves, Amer. J. Math. 90 (1968), 1201–1208.MathSciNetCrossRefGoogle Scholar
  5. 5.
    M. S. Narasimhan and S. Ramanan, Moduli of vector bundles on a compact Riemann surface, Ann. of Math. 89 (1969), 19–51.MathSciNetCrossRefGoogle Scholar
  6. 6.
    M. S. Narasimhan and S. Ramanan, Vector bundles on curves, Proceedings of the Bombay Colloquium of Algebraic Geometry, 335–346, Oxford University Press, 1969.Google Scholar
  7. 7.
    M. S. Narasimhan and C. S. Seshadri, Stable and Unitary vector bundles on a compact Riemann surface, Ann. of Math. 82 (1965), 540–567.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    P. E. Newstead, Topological properties of some spaces of stable bundles, Topology 6 (1967), 241–262.MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    P. E. Newstead, Stable bundles of rank 2 and odd degree over a curve of genus 2, Topology 7 (1968), 205–215.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    P. E. Newstead, Characteristic classes of stable bundles of rank 2 over an algebraic curve, Trans. Amer. Math. Soc. 169 (1972), 337–345.MathSciNetMATHGoogle Scholar
  11. 11.
    P. E. Newstead, Rationality of moduli spaces of stable bundles, to appear.Google Scholar
  12. 12.
    C. S. Seshadri, Space of unitary vector bundles on a compact Riemann surface, Ann. of Math. 85 (1967), 303–336.MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    C. S. Seshadri, Moduli of TT-vector bundles over an algebraic curve, Questions on Algebraic Varieties, Roma, 1970.Google Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • Raoul Bott
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

Personalised recommendations