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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On diffeomorphisms over $ T\sp 2$-knots


Author: Susumu Hirose
Journal: Proc. Amer. Math. Soc. 119 (1993), 1009-1018
MSC: Primary 57Q45
MathSciNet review: 1155598
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Abstract: For a spun $ {T^2}$-knot $ ({S^4},S(k))$ or a twisted spun $ {T^2}$-knot $ ({S^4},\tilde S(k))$ of a nontrivial knot $ k$ in $ {S^3}$, there are infinitely many isotopy classes of embeddings of a $ 2$-torus into a $ 4$-sphere which have this $ {T^2}$-knot as their image. This is shown by solving the following question: Which isotopy classes of diffeomorphisms of $ S(k)$ or $ ({S^4},\tilde S(k))$ have orientation-preserving diffeomorphisms of $ {S^4}$ as their extension?


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1155598-1
PII: S 0002-9939(1993)1155598-1
Article copyright: © Copyright 1993 American Mathematical Society