Geodesic
The Sphericity of Higher Dimensional Knots
Canadian journal of mathematics, Tome 25 (1973) no. 6, pp. 1132-1136

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In 1956 CD. Papakyriakopoulos showed [5] that the complement C of a 1-sphere S 1 tamely imbedded in a 3-sphere S 3 is aspherical; that is, that for all i ≧ 2, πi(C) = 0. In this note we show that for n ≧ 2 the complement C of an n-sphere Sn smoothly imbedded in Sn+2 is aspherical only if the fundamental group of C is infinite cyclic. Combined with results of J. Stallings [6] or of J. Levine [3], this implies that if the complement of an Sn smoothly imbedded in Sn+2 is aspherical, n ≥ 4 , then Sn is topologically unknotted in Sn+2. 
Dyer, Eldon; Vasquez, A. T. The Sphericity of Higher Dimensional Knots. Canadian journal of mathematics, Tome 25 (1973) no. 6, pp. 1132-1136. doi: 10.4153/CJM-1973-121-5
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