This is an example from Bott and Tu 's book DFAT(page 125).The example is in the image.I don't understand why can we get the local degree of the section s by constructing an vector field by parallel translation and calculate the rotating number of it.And why the local degree is 2?(adsbygoogle = window.adsbygoogle || []).push({});

Could anybody recommend me a book on it?Thank you!

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# The Euler class of the unit tangent bundle to S^2

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