Exotic smooth structures on 4-manifolds with zero signature

TL;DR

This paper constructs infinite families of distinct smooth structures on specific 4-manifolds, expanding the understanding of exotic smooth structures in four-dimensional topology.

Contribution

It introduces new methods to produce infinitely many non-diffeomorphic smooth structures on certain 4-manifolds with zero signature.

Findings

Infinite families of mutually nondiffeomorphic smooth structures constructed.

Applicable to connected sums of multiple copies of $S^2\times S^2$ and $\CP#\CPb$.

Advances the classification of smooth structures on 4-manifolds.

Abstract

For every integer $k\geq 2$, we construct infinite families of mutually nondiffeomorphic irreducible smooth structures on the topological $4$-manifolds $(2k-1)(S^2\times S^2)$ and $(2k-1)(\CP#\CPb)$, the connected sums of $2k-1$ copies of $S^2\times S^2$ and $\CP#\CPb$.