Theoretical and Mathematical Physics

, Volume 164, Issue 3, pp 1140–1150 | Cite as

Harmonic spheres conjecture

  • A. G. Sergeev


We discuss the harmonic spheres conjecture that the space of harmonic maps of the Riemann sphere into the loop space of a compact Lie group G are related to the moduli space of Yang-Mills G-fields on the four-dimensional Euclidean space.


harmonic map Yang-Mills field loop space twistor space 


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  1. 1.
    M. F. Atiyah, Comm. Math. Phys., 93, 437–451 (1984).MATHCrossRefMathSciNetADSGoogle Scholar
  2. 2.
    S. K. Donaldson, Comm. Math. Phys., 93, 453–460 (1984).MATHCrossRefMathSciNetADSGoogle Scholar
  3. 3.
    M. Atiyah, The Geometry and Physics of Knots, Cambridge Univ. Press, Cambridge (1990).MATHCrossRefGoogle Scholar
  4. 4.
    M. F. Atiyah, N. J. Hitchin, and I. M. Singer, Proc. Roy. Soc. London A, 362, 425–461 (1978).MATHCrossRefMathSciNetADSGoogle Scholar
  5. 5.
    J. Eells and S. Salamon, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 12, 589–640 (1985).MATHMathSciNetGoogle Scholar
  6. 6.
    F. E. Burstall and S. M. Salamon, Math. Ann., 277, 249–265 (1987).MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    A. Pressley and G. Segal, Loop Groups, Clarendon, Oxford (1986).MATHGoogle Scholar

Copyright information

© MAIK/Nauka 2010

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRASMoscowRussia

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