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

Authors: J. L. Bryant and R. C. Lacher
Journal: Trans. Amer. Math. Soc. 164 (1972), 333-339
MSC: Primary 57A35
DOI: https://doi.org/10.1090/S0002-9947-1972-0293641-3
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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