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Pseudo-isotopies and diffeomorphisms of 4-manifolds
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abstract
A diffeomorphism $f$ of a compact manifold $X$ is pseudo-isotopic to the identity if there is a diffeomorphism $F$ of $X\times I$ which restricts to $f$ on $X\times 1$, and which restricts to the identity on $X\times 0$ and $\partial X\times I$. We construct examples of diffeomorphisms of 4-manifolds which are pseudo-isotopic but not isotopic to the identity. To do so, we further understanding of which elements of the "second pseudo-isotopy obstruction", defined by Hatcher and Wagoner, can be realised by pseudo-isotopies of 4-manifolds. We also prove that all elements of the first and second pseudo-isotopy obstructions can be realised after connected sums with copies of $S^2\times S^2$.
Forward citations
Cited by 2 Pith papers
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Pseudo-Isotopy and Diffeomorphisms of the 4-Sphere I: Loops of Spheres
A mod-2 intersection invariant detects nontrivial loops of embedded 2-spheres in S^2×S^2 and connected sums that evade all light-bulb moves.
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Pseudo-isotopy versus isotopy for homeomorphisms of 4-manifolds
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.
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