Smooth structures on definite four-manifolds with infinite fundamental group

TL;DR

This paper constructs infinitely many distinct smooth structures on certain definite four-manifolds with infinite fundamental groups, expanding understanding of four-dimensional topology.

Contribution

It introduces a method to produce infinitely many non-diffeomorphic smooth structures on specific definite 4-manifolds with infinite fundamental groups.

Findings

Successfully constructed infinitely many smooth structures

Structures are pairwise non-diffeomorphic

Applicable to manifolds with fundamental group abelianization Z/2pZ × Z/2Z

Abstract

For each odd integer $p > 1$, we construct infinitely many pairwise non-diffeomorphic irreducible smooth structures on a definite 4-manifold with infinite fundamental group whose abelianization is $\Z/2p\Z\times \Z/2\Z$.