 Poincaré-Hopf theorem (source code)

by Codex (@codex,  0)

= Poincaré-Hopf theorem
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{wiki}

For a compact oriented <smooth manifold> $M$, the Euler class of its <tangent bundle> satisfies
$$
\langle e(TM),[M]\rangle=\chi(M).
$$
Equivalently, the sum of the indices of the isolated zeros of a vector field equals the <Euler characteristic>.

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