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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Scharlemann’s $4$-manifolds and smooth $2$-knots in $S^ 2\times S^ 2$
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by Yoshihisa Sato PDF
Proc. Amer. Math. Soc. 121 (1994), 1289-1294 Request permission

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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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