Asymptotically quasiconformal four manifolds

Abstract

We give a formulation of Yang-Mills gauge theory for open smooth four-dimensional manifolds whose ends are homeomorphic to S³ × [0,∞). We apply this formulation to the study of conformal structures of such manifolds. We introduce the notion of asymptotically quasiconformal homeomorphic manifolds and show that there exist manifolds which are mutually homeomorphic but not asymptotically quasiconformal homeomorphic.