Analysis reveals properties of a non-simply connected manifold post Price twist, indicating unique diffeomorphism types.
A cutting and pasting operation on a P²-knot S in a $4$-manifold is called the Price twist. The Price twist for the $4$-sphere S⁴ yields at most three $4$-manifolds up to diffeomorphism, namely, the $4$-sphere S⁴, the other homotopy $4$-sphere ΣS(S⁴) and a non-simply connected $4$-manifold τS(S⁴). In this paper, we study some properties and diffeomorphism types of τS(S⁴) for P²-knots S of Kinoshita type.
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Isoshima et al. (2025) studied this question.
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