  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].
