Self-Dual metrics on non-simply connected 4-manifolds

TL;DR

This paper constructs specific self-dual metrics on non-simply connected 4-manifolds, expanding understanding of their geometric structures and addressing a problem posed by Besse.

Contribution

It introduces new examples of self-dual metrics on non-simply connected 4-manifolds with small signature, including sequences with varying topological invariants.

Findings

Existence of self-dual metrics on non-simply connected 4-manifolds

Construction of sequences with bounded or unbounded Betti numbers

Metrics with negative scalar curvature

Abstract

We construct self-dual(SD) but not locally conformally flat(LCF) metrics on families of non-simply connected 4-manifolds with small signature. We construct various sequences with bounded or unbounded Betti numbers and Euler characteristic. These metrics have negative scalar curvature. As an application, this addresses the Remark 4.79 of Besse.