Solid angles and Seifert hypersurfaces
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 $M$.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2017
- DOI:
- 10.48550/arXiv.1706.06405
- arXiv:
- arXiv:1706.06405
- Bibcode:
- 2017arXiv170606405B
- Keywords:
-
- Mathematics - Geometric Topology;
- Mathematics - Differential Geometry;
- 57Q45;
- 57R40
- E-Print:
- 34 pages, 8 figures