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Proceedings of the American Mathematical Society

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Smooth $ 2$-knots in $ S\sp 2\times S\sp 2$ with simply-connected complements are topologically unique


Author: Yoshihisa Sato
Journal: Proc. Amer. Math. Soc. 105 (1989), 479-485
MSC: Primary 57Q45; Secondary 57N13, 57R40
DOI: https://doi.org/10.1090/S0002-9939-1989-0940880-X
MathSciNet review: 940880
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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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DOI: https://doi.org/10.1090/S0002-9939-1989-0940880-X
Keywords: $ 2$-knot, $ {S^2} \times {S^2}$
Article copyright: © Copyright 1989 American Mathematical Society

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