Non-smoothable homeomorphisms of $4$-manifolds with boundary

Daniel Galvin; Roberto Ladu

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arXiv · 2310.08666

Non-smoothable homeomorphisms of $4$-manifolds with boundary

Daniel Galvin·Roberto Ladu

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Abstract

We construct the first examples of non-smoothable self-homeomorphisms of smooth $4$-manifolds with boundary that fix the boundary and act trivially on homology. As a corollary, we construct self-diffeomorphisms of $4$-manifolds with boundary that fix the boundary and act trivially on homology but cannot be isotoped to any self-diffeomorphism supported in a collar of the boundary and, in particular, are not isotopic to any generalised Dehn twist.

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Daniel Galvin, Roberto Ladu. 2023-10-12. Non-smoothable homeomorphisms of $4$-manifolds with boundary. https://arxiv.org/abs/2310.08666

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