An open collar theorem for 4-manifolds

Guilbault, Craig R.

doi:10.1090/S0002-9947-1992-1038016-7

An open collar theorem for $4$-manifolds
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Trans. Amer. Math. Soc. 331 (1992), 227-245 Request permission

Abstract:

Let ${M^4}$ be an open $4$-manifold with boundary. Conditions are given under which ${M^4}$ is homeomorphic to $\partial M \times [0,1)$. Applications include a $4$-dimensional weak $h$-cobordism theorem and a classification of weakly flat embeddings of $2$-spheres in ${S^4}$. Specific examples of $(n - 2)$-spheres embedded in ${S^n}$ (including $n = 4$) are also discussed.

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