Scharlemann’s $4$-manifolds and smooth $2$-knots in $S^ 2\times S^ 2$
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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 ${S^2} \times {S^2}$.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- 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