Exotic definite four-manifolds with non-trivial fundamental group

TL;DR

This paper constructs infinitely many exotic smooth structures on certain closed four-manifolds with definite intersection form and fundamental group Z/2Z, expanding the understanding of smooth structures in four-dimensional topology.

Contribution

It introduces new methods to produce exotic smooth structures on four-manifolds with fundamental group Z/2Z, including cases with even b_2^+.

Findings

Infinite exotic smooth structures constructed

Examples include manifolds with even b_2^+

Expands the class of known exotic four-manifolds

Abstract

Inspired by a recent result of Levine-Lidman-Piccirillo, we construct infinitely many exotic smooth structures on some closed four-manifolds with definite intersection form and fundamental group isomorphic to $\Z /2\Z$. Similar constructions provide exotic smooth structures on further four-manifolds with fundamental group $Z/2\Z$, including examples with even $b_2^+$.