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Irreducibility of the closed 4–manifolds constructed in Theorem \ref{thm: closed}

Ascertain whether the closed 4–manifolds produced in Theorem \ref{thm: closed} are irreducible.

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Background

Theorem \ref{thm: closed} constructs closed 4–manifolds admitting infinite-order exotic diffeomorphisms via a gluing framework involving symplectic fillings and mapping torus techniques.

While this produces the desired exotic diffeomorphisms, the authors note explicitly that they do not know whether these specific closed 4–manifolds are irreducible, highlighting a concrete unresolved aspect of their construction.

References

While we do not know whether the closed 4-manifolds in Theorem \ref{thm: closed} are irreducible, Theorem \ref{thm: closed} provides a systematic way to produce (infinite order) exotic diffeomorphisms of closed 4-manifolds, which is different from the known technique pioneered by Ruberman using exotic pairs of closed 4-manifolds.

— On four-dimensional Dehn twists and Milnor fibrations (2409.11961 - Konno et al., 18 Sep 2024) in Introduction, Subsection “Exotic Dehn twists on open, contractible, and closed manifolds”