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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

An open collar theorem for $ 4$-manifolds


Author: Craig R. Guilbault
Journal: Trans. Amer. Math. Soc. 331 (1992), 227-245
MSC: Primary 57N13; Secondary 57N40, 57N45
DOI: https://doi.org/10.1090/S0002-9947-1992-1038016-7
MathSciNet review: 1038016
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1038016-7
Keywords: Open collar, $ 4$-manifold, weakly flat, $ 1$-alg, wild embedding, weak $ h$-cobordism theorem
Article copyright: © Copyright 1992 American Mathematical Society