Orientability of sphere

  • Thread starter mritunjay
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  • #1
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Is the atlas for the sphere consisting of the stereographic projections from north and south pole is an orientable atlas.
 

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  • #2
tiny-tim
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hi mritunjay! :smile:

what is the definition of orientable? :wink:

(alternatively, what is the definition of non-orientable?)
 
  • #3
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a sphere is orientable if and only if it admits a volume form. If you're in a Riemannian manifold then the volume form is well known. Or you can use the definition of orientability of a manifold, a manifold is orientable if \ det (\ frac {\ partial x ^ {i}} {{partial y ^ {i}})> 0 for two coordinate system x ^ {i} and y ^ {i} on the variety.
 

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