Pseudo-isotopy versus isotopy for homeomorphisms of 4-manifolds

Daniel Galvin; Isacco Nonino

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arXiv · 2506.11905

Pseudo-isotopy versus isotopy for homeomorphisms of 4-manifolds

Daniel Galvin·Isacco Nonino

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Abstract

We define obstructions which obstruct topological pseudo-isotopies from being isotopic to isotopies in dimension four. These match the smooth obstructions of Hatcher-Wagoner for smooth pseudo-isotopies, and accordingly are valued in certain Whitehead groups. We show that our obstructions are fully realisable, and we use these realisations to build homeomorphisms of $Y\times S^1$ for many 3-manifolds $Y$ that are pseudo-isotopic to the identity but not isotopic to the identity.

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BibTeX RIS

Daniel Galvin, Isacco Nonino. 2025-06-13. Pseudo-isotopy versus isotopy for homeomorphisms of 4-manifolds. https://arxiv.org/abs/2506.11905

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