# Solid angles and Seifert hypersurfaces

## TL;DR

This paper investigates the properties of the solid angle function associated with a smooth closed oriented manifold embedded in Euclidean space, revealing that non-critical level sets form explicit Seifert hypersurfaces.

## Contribution

It establishes a connection between the solid angle function and Seifert hypersurfaces, providing explicit constructions in higher dimensions.

## Key findings

- Non-critical level sets of the solid angle function are Seifert hypersurfaces.
- The paper characterizes properties of the solid angle function for embedded manifolds.
- Provides explicit descriptions of Seifert hypersurfaces in higher dimensions.

## 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 $M$.