Knots and links of complex tangents

Naohiko Kasuya; Masamichi Takase

doi:10.1090/tran/7164

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arXiv · 1606.03704

Knots and links of complex tangents

Naohiko Kasuya·Masamichi Takase

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Abstract

It is shown that every knot or link is the set of complex tangents of a 3-sphere smoothly embedded in the three-dimensional complex space. We show in fact that a one-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 three-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.

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BibTeX RIS

Naohiko Kasuya, Masamichi Takase. 2016-06-27. Knots and links of complex tangents. https://doi.org/10.1090/tran%2F7164

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