Exotic structures on 4-manifolds with infinite dihedral fundamental group

TL;DR

This paper constructs infinitely many exotic smooth structures on certain 4-manifolds with infinite dihedral fundamental group, expanding understanding of smooth topology in four dimensions under specific Betti number conditions.

Contribution

It introduces new methods to produce infinite exotic structures on 4-manifolds with infinite dihedral fundamental group, given certain Betti number constraints.

Findings

Existence of infinitely many exotic structures on these 4-manifolds.

Conditions on Betti numbers for the constructions.

Extension of exotic structure techniques to non-simply connected manifolds.

Abstract

The aim of this paper is to produce infinite exotic structures on smooth closed oriented $4-$manifolds with fundamental group isomorphic to the infinite dihedral group, assuming that $b_2^+$ and $b_2^-$ are at least $12$.