Monopoles,braid groups,and the dirac operator |
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Authors: | Ralph L Cohen John D S Jones |
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Institution: | (1) Department of Mathematics, Stanford University, 94305 Stanford, CA, USA;(2) Mathematics Institute, University of Warwick, CV4 7AL Coventry, England |
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Abstract: | Using the relation between the space of rational functions on , the space ofSU(2)-monopoles on 3, and the classifying space of the braid group, see 10], we show how the index bundle of the family of real Dirac operators coupled toSU(2)-monopoles can be described using permutation representations of Artin's braid groups. We also show how this implies the existence of a pair consisting of a gauge fieldA and a Higgs field on 3 whose corresponding Dirac equation has an arbitrarily large dimensional space of solutions.The first author was supported by a grant from the NSF |
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