A 1-ALG Simple Closed Curve in E3 is Tame

Abstract

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.