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A 1-ALG Simple Closed Curve in E3 is Tame

Published online by Cambridge University Press:  20 November 2018

W. S. Boyd  and
A. H. Wright
W. S. Boyd
Affiliation:
Western Michigan University, Kalamazoo, Michigan
A. H. Wright
Affiliation:
Western Michigan University, Kalamazoo, Michigan
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Let J be a simple closed curve in a 3-manifold M3. We say M — J is 1-ALG at p ∈ J (or has locally abelian fundamental group at p) if and only if for each sufficiently small open set U containing p, there is an open set V such that p ∈ V ⊂ U and each loop in V — J which bounds in U — J is contractible to a point in U — J.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 3 , June 1973 , pp. 646 - 656
Copyright
Copyright © Canadian Mathematical Society 1973

References

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