Understanding S^2 as the Quotient of SO(3) and SO(2)

[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?

 

[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.

 

[Lonewolf]

Thanks, it helped having something to search for!