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S^2 and homogeneous spaces

  1. Apr 20, 2005 #1
    I've seen [itex]S^2[/itex] written as the quotient [itex]SO(3)/SO(2)[/itex]. Can someone run me through how to show this, or point to somewhere that does, as I've only seen it stated?
     
  2. jcsd
  3. Apr 20, 2005 #2

    matt grime

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    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.
     
  4. Apr 20, 2005 #3
    Thanks, it helped having something to search for!
     
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