Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have an exercise which says that :extend the Hopf-Poincare theorem for non-orientable manifold with the indication using the double covering. I have got stuck for long time, so I don't know if somebody can help me. Any answer is greatly appreciated.

share|cite|improve this question
1) Pull the vector field back to the double cover 2) apply the orientable Poincaré-Hopf theorem 3) divide by two. Since the index is local in nature, this won't change the index of a zero (and each original zero corresponds to two zeroes on the double cover). The Euler characteristic is multiplicative with respect to $n$-sheeted coverings. – commenter Oct 17 '12 at 16:16
Thanks! I get a lot! – mapping Oct 18 '12 at 8:32

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.