The non-simply connected Price twist for the 4-sphere

2025/05/14 by Isoshima, Tsukasa, Suzuki, Tatsumasa
#57K10 #57K40 #57K45 #57R65 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2505.09332

Abstract

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 Σ_S(S⁴) and a non-simply connected 4-manifold τ_S(S⁴). In this paper, we study some properties and diffeomorphism types of τ_S(S⁴) for P²-knots S of Kinoshita type.

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