This paper outlines in an informal and intuitive fashion a method for computing the second homotopy group p2(X) (as a left Zp1(X) -module) of the complement X = S5 - kM3 of a smooth 3-knot (S5, kM3). By a smooth 3-knot (S5, kM3) is meant a smooth imbedding of a closed 3-manifold M3 in the 5-sphere S5 . An example of the calculation is given.
The methods of this paper may also be used to compute the Rohlin invariant of 3-manifolds from their imbeddings in S5 .
(*) Partially supported by the L-O-O-P Fund.