MISC

2018年

Knots and links of complex tangents

Transactions of the American Mathematical Society
  • Naohiko Kasuya
  • ,
  • Masamichi Takase

370
3
開始ページ
2023
終了ページ
2038
記述言語
英語
掲載種別
DOI
10.1090/tran/7164
出版者・発行元
American Mathematical Society

It is shown that every knot or link is the set of complex tangents of a 3-sphere smoothly embedded in the 3-dimensional complex space. We show in fact that a 1-dimensional submanifold of a closed orientable 3-manifold can be realised as the set of complex tangents of a smooth embedding of the 3-manifold into the 3-dimensional complex space if and only if it represents the trivial integral homology class in the 3-manifold. The proof involves a new application of singularity theory of differentiable maps.

リンク情報
DOI
https://doi.org/10.1090/tran/7164
URL
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85039795088&origin=inward

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