Determine whether the constructed exotic smooth structures coincide with previously constructed ones

Determine whether the exotic smooth structures on the universal covers constructed in this paper are diffeomorphic to the exotic smooth structures constructed in Akhmedov–Sakallı–Yeung, Akhmedov–Sakallı, and Akhmedov–Park–Yeung.

Background

The paper constructs, for every integer m≥2, symplectic four-manifolds whose universal covers are exotic smooth manifolds homeomorphic to connected sums of complex projective planes and oppositely oriented complex projective planes. The authors compare these examples with exotic smooth structures obtained in several earlier works, including constructions with related intersection forms and signatures.

The unresolved issue is whether the exotic smooth structures produced here are genuinely distinct, up to diffeomorphism, from the exotic smooth structures in the cited earlier constructions. The paper establishes the relevant homeomorphism types and exoticness relative to the standard connected sums, but does not determine diffeomorphism equivalence with those previously constructed exotic examples.