Cyclic Monopoles, Affine Toda and Spectral Curves

We show that any cyclically symmetric monopole is gauge equivalent to Nahm data given by Sutcliffe's ansatz, and so obtained from the affine Toda equations. Further the direction (the Ercolani-Sinha vector) and base point of the linearising flow in the Jacobian of the spectral curve associated to the Nahm equations arise as pull-backs of Toda data. A theorem of Accola and Fay then means that the theta-functions arising in the solution of the monopole problem reduce to the theta-functions of Toda.Comment: 18 page

Functional Equations and the Generalised Elliptic Genus

We give a new derivation and characterisation of the generalised elliptic genus of Krichever-H\"ohn by means of a functional equation.Comment: To be published in the collection honouring Francesco Calogero's 70-th birthda