3-Spheres in the 4-Sphere and Pseudo-Isotopies of $S^1\times S^3$

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arxiv 2212.02004 v2 pith:PDBLLQBH submitted 2022-12-05 math.GT

David Gabai This is my paper · ORCID

classification math.GT

keywords approachconjecturedimensionalofferpseudo-isotopiespseudo-isotopyschoenfliessmooth

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We offer an approach to the smooth 4-dimensional Schoenflies conjecture via pseudo-isotopy theory.

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Smoothing topological pseudo-isotopies of 4-manifolds
math.GT 2025-07 accept novelty 8.0 of 10

The paper proves a Kirby-Siebenmann obstruction criterion for smoothing topological pseudo-isotopies of 4-manifolds, gives new positive cases for certain fundamental groups, and constructs the first diffeomorphisms th...
Pseudo-isotopy versus isotopy for homeomorphisms of 4-manifolds
math.GT 2025-06 conditional novelty 7.0 of 10

A topological version of the Hatcher-Wagoner pseudo-isotopy obstructions is defined in dimension four and used to construct homeomorphisms of Y times S1 that are pseudo-isotopic but not isotopic to the identity.