Exotic definite four-manifolds with non-cyclic fundamental group

TL;DR

This paper constructs infinitely many distinct smooth structures on a specific definite four-manifold with a non-cyclic fundamental group, expanding understanding of four-manifold topology.

Contribution

It introduces new examples of definite four-manifolds with non-cyclic fundamental groups and demonstrates the existence of infinitely many non-diffeomorphic smooth structures.

Findings

Existence of infinitely many smooth structures on a definite 4-manifold with non-cyclic fundamental group.

Construction method for such smooth structures.

Non-diffeomorphic nature of the constructed structures.

Abstract

We construct infinitely many pairwise non-diffeomorphic smooth structures on a definite $4$-manifold with non-cyclic fundamental group $\mathbb{Z}/2\times \mathbb{Z}/2$.