Poincaré–Hopf theorem

Summary

Poincaré–Hopf theorem is a theorem^[1]. It draws 116 Wikipedia views per month (theorem category, ranking #181 of 1,306).^[2]

Key Facts

• Poincaré–Hopf theorem's instance of is recorded as theorem^[3].
• Henri Poincaré is named after Poincaré–Hopf theorem^[4].
• Heinz Hopf is named after Poincaré–Hopf theorem^[5].
• Poincaré–Hopf theorem's part of is recorded as list of theorems^[6].
• Poincaré–Hopf theorem's Freebase ID is recorded as /m/04nm34^[7].
• Poincaré–Hopf theorem's proved by is recorded as Heinz Hopf^[8].
• Poincaré–Hopf theorem's defining formula is recorded as \sum_{x\in M\atop v(x)=0}\deg_{\partial\operatorname{ball}(x,\epsilon)\to\mathbb S^{\dim M-1}}\left(y\mapsto\frac{v(y)}{|v(y)|}\right)=\chi (M)^[9].
• Poincaré–Hopf theorem's nLab ID is recorded as Poincaré–Hopf theorem^[10].
• Poincaré–Hopf theorem's maintained by WikiProject is recorded as WikiProject Mathematics^[11].
• Poincaré–Hopf theorem's Microsoft Academic ID is recorded as 2780799127^[12].
• Poincaré–Hopf theorem's in defining formula is recorded as M^[13].
• Poincaré–Hopf theorem's in defining formula is recorded as v^[14].
• Poincaré–Hopf theorem's in defining formula is recorded as \chi(-)^[15].
• Poincaré–Hopf theorem's in defining formula is recorded as \deg(-)^[16].
• Poincaré–Hopf theorem's in defining formula is recorded as \mathbb S^n^[17].
• Poincaré–Hopf theorem's in defining formula is recorded as x^[18].
• Poincaré–Hopf theorem's in defining formula is recorded as v(y)/|v(y)|^[19].
• Poincaré–Hopf theorem's Encyclopedia of Mathematics article ID is recorded as Poincaré-Hopf_theorem^[20].

Why It Matters

Poincaré–Hopf theorem draws 116 Wikipedia views per month (theorem category, ranking #181 of 1,306).^[2] It has Wikipedia articles in 11 language editions, a strong signal of global cultural recognition.^[21] It is known by 14 alternative names across languages and contexts.^[22]