On the diffeomorphism groups of rational and ruled 4-manifolds

Abstract

Let $A(M)$ be the automorphism group of the middle homology of a smooth 4-manifold $M$ and $D(M)$ be the subgroup induced by diffeomorphisms of $M$. In this paper we give explicit generators of $D(M)$ for rational and ruled 4-manifolds. We also prove the uniqueness of reduced forms for classes with minimal genus 0 and non-negative square.