# S^2 and homogeneous spaces

1. Apr 20, 2005

### Lonewolf

I've seen $S^2$ written as the quotient $SO(3)/SO(2)$. Can someone run me through how to show this, or point to somewhere that does, as I've only seen it stated?

2. Apr 20, 2005

### matt grime

It's called the Hopf fibration. There are many ways to realize it, one of which uses quarternions I recall. Anyway, a google for hopf fibration will give you more than I can remember off the top of my head, and there's even an animation illustrating it somewhere.

3. Apr 20, 2005

### Lonewolf

Thanks, it helped having something to search for!