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I was wondering if there was a prove of the Poincaré-Hopf index theorem using Gauss-Bonnet I'll really like to see one to understand it better.

GDumphart
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HelaHelheim
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    There is, see section $2.2$ in Li's paper http://www.maths.ed.ac.uk/~aar/papers/li4.pdf –  Nov 24 '16 at 08:51

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