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 that are topologically but not smoothly pseudo-isotopic to the identity.
Pseudo-isotopy versus isotopy for homeomorphisms of 4-manifolds
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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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Smoothing topological pseudo-isotopies of 4-manifolds
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 that are topologically but not smoothly pseudo-isotopic to the identity.