MONOPOLES, BRAID-GROUPS, AND THE DIRAC OPERATOR

Using the relation between the space of rational functions on C, the s pace of SU(2)-monopoles on R3, and the classifying space of the braid group, see [10], we show how the index bundle of the family of real Di rac operators coupled to SU(2)-monopoles can be described using permut ation representations of Artin's braid groups. We also show how this i mplies the existence of a pair consisting of a gauge field A and a Hig gs field PHI on R3 whose corresponding Dirac equation has an arbitrari ly large dimensional space of solutions.