For each knot K ⊂ S 3 and a 4-manifold X that satisfies certain conditions, we use Fintushel-Stern's knot surgery to construct a nullhomotopic 2-sphere S K ⊂ X#S 2 × S 2 such that S K bounds a topologically embedded handlebody, i.e., S K is topologically isotopic to an unknotted 2-sphere contained in a 4-ball. If there is a diffeomorphism of pairs (X#S 2 × S 2 , S K1 ) → (X#S 2 × S 2 , S K2 ), then the knots K 1 and K 2 have the same Alexander polynomial. In particular, the construction in this note yields an infinite set of topologically unknotted nullhomotopic 2-spheres in X#S 2 × S 2 and an infinite set of topologically equivalent 2-disks in X#S 2 × S 2 \ D 4 that are smoothly inequivalent, and for which the diffeomorphism types of the embeddings are detected by the Alexander polynomial. Examples of knotted behaviour of 2-spheres in 4-manifolds that is detected by the Reidemeister/Turaev torsion of lens spaces are also provided.
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