Mapping cylinder neighborhoods of one-complexes in four-space

Bryant, J. L.; Lacher, R. C.

doi:10.1090/S0002-9947-1972-0293641-3

Mapping cylinder neighborhoods of one-complexes in four-space
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by J. L. Bryant and R. C. Lacher PDF

Trans. Amer. Math. Soc. 164 (1972), 333-339 Request permission

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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Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten

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properties and related topics

Victor Nicholson, Mapping cylinder neighborhoods, Trans. Amer. Math. Soc. 143 (1969), 259–268. MR 248788, DOI 10.1090/S0002-9947-1969-0248788-4

Mappings from

manifolds onto

manifolds