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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Mapping cylinder neighborhoods of one-complexes in four-space


Authors: J. L. Bryant and R. C. Lacher
Journal: Trans. Amer. Math. Soc. 164 (1972), 333-339
MSC: Primary 57A35
MathSciNet review: 0293641
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Abstract: We prove the following theorem: If K is a 1-complex topologically embedded in $ {S^4}$, and if K has mapping cylinder neighborhoods in $ {S^4}$ at almost all of its points, then K is tame. The proof uses engulfing and the theory of proper, one-acyclic mappings of 3-manifolds onto the real line.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0293641-3
PII: S 0002-9947(1972)0293641-3
Keywords: Topological embeddings of one-complexes, locally flat embeddings, locally tame embeddings, mapping cylinder neighborhoods, UV properties, engulfing
Article copyright: © Copyright 1972 American Mathematical Society