Fundamental group of self-dual four-manifolds with positive scalar curvature

Abstract

In the first part of the paper we show in a very simple manner that the fundamental groups of four-manifolds with a self-dual metric of positive scalar curvature admit a surjective homomorphism on ℤ, if there is a nontrivial representation. In the second part we outline a method how to construct negatively curved metrics in Taubs collars.