Classification and existence of doubly-periodic instantons

Abstract

We present a classification of SU(2) instantons on $T^2\times {\mathbb{R}}^2$ according to their asymptotic behaviour. We then study the existence of such instantons for different values of the asymptotic parameters, describing explicitly the moduli space for unit charge.

Significant changes made to the text, though results are essentially the same. Version to appear on Quart. J. Math. 17 pages, 2 figures