Abstract
We discuss the harmonic spheres conjecture, relating the space of harmonic maps of the Riemann sphere into the loop space of a compact Lie group G with the moduli space of Yang–Mills G-fields on four-dimensional Euclidean space.
Mathematics Subject Classification (2010). Primary 58E20, 53C28,32L25.
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References
M.F. Atiayh, Instantons in two and four dimensions. Comm. Math. Phys. 93 (1984), 437–451.
M.F. Atiayh, N.J. Hitchin, I.M. Singer, Self-duality in four-dimensional Riemannian geometry. Proc. Roy. Soc. London 362 (1978), 425–461.
F.E. Burstall, S. Salamon, Tournaments, flags and harmonic maps. Math. Ann. 277 (1987), 249–265.
S.K. Donaldson, Instantons and geometric invariant theory. Comm. Math. Phys. 93 (1984), 453–460.
J. Eells, S. Salamon, Twistorial constructions of harmonic maps of surfaces into four-manifolds. Ann. Scuola Norm. Super. Pisa 12 (1985), 589–640.
A. Pressley, G. Segal, Loop Groups. Clarendon Press, 1986.
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Sergeev, A. (2014). Harmonic Spheres Conjecture. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodríguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_29
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DOI: https://doi.org/10.1007/978-3-0348-0648-0_29
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