Solid angles and Seifert hypersurfaces

Maciej Borodzik; Supredee Dangskul; Andrew Ranicki

Solid angles and Seifert hypersurfaces

Geometric Topology 2017-06-21 v1 Differential Geometry

Authors: Maciej Borodzik , Supredee Dangskul , Andrew Ranicki

Abstract

Given a smooth closed oriented manifold $M$ of dimension $n$ embedded in $\mathbb{R}^{n+2}$ we study properties of the `solid angle' function $\Phi\colon\mathbb{R}^{n+2}\setminus M\to S^1$ . It turns out that a non-critical level set of $\Phi$ is an explicit Seifert hypersurface for $M$ .

Keywords

hypersurfaces surfaces and embeddings morse theory

Cite

@article{arxiv.1706.06405,
  title  = {Solid angles and Seifert hypersurfaces},
  author = {Maciej Borodzik and Supredee Dangskul and Andrew Ranicki},
  journal= {arXiv preprint arXiv:1706.06405},
  year   = {2017}
}

Comments

34 pages, 8 figures

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