On absolutely exotic diffeomorphisms of 4-manifolds

Hokuto Konno; Abhishek Mallick; Masaki Taniguchi

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arXiv · 2510.05505

On absolutely exotic diffeomorphisms of 4-manifolds

Hokuto Konno·Abhishek Mallick·Masaki Taniguchi

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Abstract

We prove that there exist infinitely many contractible compact smooth $4$-manifolds $C$ that admit absolutely exotic diffeomorphisms of infinite order in $\pi_0(\mathrm{Diff}(C))$. By ``absolutely", we mean that isotopies are not required to be relative to the boundary. This follows from a theorem that produces absolutely exotic diffeomorphisms from relatively exotic diffeomorphisms, analogous to a theorem of Akbulut and Ruberman that produces absolutely exotic 4-manifolds from relatively exotic 4-manifolds.

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Hokuto Konno, Abhishek Mallick, Masaki Taniguchi. 2025-10-07. On absolutely exotic diffeomorphisms of 4-manifolds. https://arxiv.org/abs/2510.05505

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