Abstract
The configuration space for the SU(2)-Yang-Mills-Higgs equations on ℝ3 is shown to be homotopic to the space of smooth maps fromS 2 toS 2. This configuration space indexes a family of twisted Dirac operators. The Dirac family is used to prove that the configuration space does not retract onto any subspace on which the SU(2)-Yang-Mills-Higgs functional is bounded.
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Communicated by A. Jaffe
National Science Foundation Postdoctoral Fellow in Mathematics
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Taubes, C.H. Monopoles and maps fromS 2 toS 2; the topology of the configuration space. Commun.Math. Phys. 95, 345–391 (1984). https://doi.org/10.1007/BF01212403
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DOI: https://doi.org/10.1007/BF01212403