Wall's stable realization for diffeomorphisms of definite 4-manifolds

TL;DR

This paper extends Wall's 1964 result by showing that automorphisms of the intersection form of a smooth, simply connected, closed 4-manifold with definite form can be realized by diffeomorphisms after connected sum with S^2 x S^2.

Contribution

It provides a complete realization of intersection form automorphisms as diffeomorphisms for a class of 4-manifolds by using connected sums with S^2 x S^2.

Findings

Automorphisms of intersection forms are realizable by diffeomorphisms after stabilization.

Extends Wall's foundational result from 1964.

Completes the classification for definite 4-manifolds.

Abstract

Let $X$ be a smooth simply connected closed 4-manifold with definite intersection form. We show that any automorphism of the intersection form of $X$ is realized by a diffeomorphism of $X \mathbin{\#} S^2 \times S^2$. This extends and completes Wall's foundational result from 1964.