All Questions
Tagged with euler-characteristics gt.geometric-topology
1 question with no upvoted or accepted answers
2
votes
0
answers
1k
views
What kinds of manifolds admit non-vanishing vector fields defining convergent congruences?
One of the corollaries of the Poincaré–Hopf index theorem is that a closed, connected manifold $M$ admits non-vanishing vector fields iff its Euler characteristic is zero; i.e. $\chi(M) = 0$.
I am ...
