三维伪合痕的第二个障碍
Second obstruction to pseudoisotopy in dimension 3
摘要：
我们利用透镜模型和伪合痕的第二个障碍构造了$M\times I$的一个非平凡同构，其中$M$是$S^1\times S^2$与另一个非单连通3-流形$M'$的连通和.然后，我们取两个该同构的副本，并将它们的顶部和底部粘贴在一起，以获得$M\times S^1$的同构。第二个障碍和第一个Postnikov不变量的性质意味着这个闭4-流形$M\times S^1$的同形不是恒等式的同位素。Singh也得到了类似的结果[10]。
英文摘要：
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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