Smooth 2-knots in 𝑆²×𝑆² with simply-connected complements are topologically unique

Sato, Yoshihisa

doi:10.1090/S0002-9939-1989-0940880-X

Smooth $2$-knots in $S^ 2\times S^ 2$ with simply-connected complements are topologically unique
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Proc. Amer. Math. Soc. 105 (1989), 479-485 Request permission

Abstract:

For a given primitive homology class $\xi$ of ${H_2}({S^2} \times {S^2};{\mathbf {Z}})$, we show that there exists only one smoothly embedded $2$-sphere in ${S^2} \times {S^2}$ , up to homeomorphism, which represents $\xi$ and whose complement is simply connected.

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