Knots and links of complex tangents
Geometric Topology
2018-03-22 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.1606.03704,
title = {Knots and links of complex tangents},
author = {Naohiko Kasuya and Masamichi Takase},
journal= {arXiv preprint arXiv:1606.03704},
year = {2018}
}