nLab equator

Idea

Given an n-sphere $S^n$, regarded under its standard embedding into Cartesian space $\mathbb{R}^{n+1}$, then its equator is the intersection with $\mathbb{R}^n \subset \mathbb{R}^{n+1}$.

The equator devides the $n$-sphere into its to hemi-n-spheres.

For $n \geq 1$, the full $n$-sphere is the suspension of its equator $(n-1)$-sphere, namely the union of all meridians passing through the equator.

Related concepts

• meridian

• hemisphere, antipode

• stereographic projection

• clutching construction