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Second obstruction to pseudoisotopy in dimension 3
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abstract
We use lens-shaped models and the second obstruction to pseudoisotopy to construct a nontrivial diffeomorphism of $M\times I$ where $M$ is the connected sum of $S^1\times S^2$ with a another nonsimply connected 3-manifold $M'$. Then we take two copies of this diffeomorphism and paste together their tops and bottoms to obtain a diffeomorphism of $M\times S^1$. Properties of the second obstruction and the first Postnikov invariant imply that this diffeomorphism of the closed 4-manifold $M\times S^1$ is not isotopic to the identity. Similar results were obtain by Singh [10].
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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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