Degenerating metrics and instantons on the four-sphere

Abstract

We give a direct proof of Atiyah's theorem relating instantons over the four-sphere with holomorphic maps from the two-sphere to the loop group. Our approach uses the non-linear heat flow equation for Hermitian metrics as used in the study of Kahler manifolds. The proof generalises immediately to a larger class of four-manifolds. Copyright © 1998 Elsevier Science B.V.