Spectral curves of non-integral hyperbolic monopoles

Abstract

The twistor desription of non-integral SUn-monopoles on hyperbolic 3-space is developed and some consequences discussed. It is shown that in a precise sense, any appropriately decaying hyperbolic monopole is determined by its asymptotic values, and also that such monopoles determine and are determined by their spectral data (which reduces to a complex algebraic curve when n = 2). This paper provides the hyperbolic analogue of the work of Hitchin and others on euclidean monopoles and generalizes that of Atiyah and Braam-Austin on integral hyperbolic monopoles. © 1996 IOP Publishing Ltd and LMS Publishing Ltd.