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Scharlemann's $ 4$-manifolds and smooth $ 2$-knots in $ S\sp 2\times S\sp 2$


Author: Yoshihisa Sato
Journal: Proc. Amer. Math. Soc. 121 (1994), 1289-1294
MSC: Primary 57Q45; Secondary 57R55
DOI: https://doi.org/10.1090/S0002-9939-1994-1218118-X
MathSciNet review: 1218118
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Abstract: Scharlemann gave an example of a 4-manifold admitting a fake homotopy structure on $ {S^3} \times {S^1}\sharp {S^2} \times {S^2}$, which is homeomorphic to $ {S^3} \times {S^1}\sharp {S^2} \times {S^2}$ by a theorem of Freedman. We address the problem whether a Scharlemann's manifold is diffeomorphic to $ {S^3} \times {S^1}\sharp {S^2} \times {S^2}$ in terms of 2-knots in $ {S^2} \times {S^2}$.


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DOI: https://doi.org/10.1090/S0002-9939-1994-1218118-X
Keywords: Scharlemann's manifold, 4-manifold, knots
Article copyright: © Copyright 1994 American Mathematical Society

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