Geodesic
A 1-ALG Simple Closed Curve in E 3 is Tame
Canadian journal of mathematics, Tome 25 (1973) no. 3, pp. 646-656

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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. 
Boyd, W. S.; Wright, A. H. A 1-ALG Simple Closed Curve in E 3 is Tame. Canadian journal of mathematics, Tome 25 (1973) no. 3, pp. 646-656. doi: 10.4153/CJM-1973-065-0
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