Poincaré–Hopf theorem ^Béarla (Q1305766)

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theorem relating the Euler characteristic of a closed manifold to the number of zeros of a vector field on it ^Béarla

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Language	Label	Description	Also known as
Gaeilge	No label defined	No description defined
Béarla	Poincaré–Hopf theorem	theorem relating the Euler characteristic of a closed manifold to the number of zeros of a vector field on it	Poincaré–Hopf index formula Poincaré–Hopf index theorem Hopf index theorem

Statements

sampla de

teoirim

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ainmnithe in ómós

Henri Poincaré

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Heinz Hopf

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foirmle

${\displaystyle \sum _{x\in M \atop v(x)=0}\deg _{\partial \operatorname {ball} (x,\epsilon )\to \mathbb {S} ^{\dim M-1}}\left(y\mapsto {\frac {v(y)}{\|v(y)\|}}\right)=\chi (M)}$

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in defining formula ^Béarla

${\displaystyle M}$

symbol represents ^Béarla

closed manifold ^Béarla

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${\displaystyle v}$

symbol represents ^Béarla

vector field ^Béarla

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${\displaystyle \chi (-)}$

symbol represents ^Béarla

dual-luach Euler

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${\displaystyle \deg(-)}$

symbol represents ^Béarla

degree of a continuous mapping ^Béarla

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${\displaystyle \mathbb {S} ^{n}}$

symbol represents ^Béarla

n-sféar

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${\displaystyle x}$

symbol represents ^Béarla

zero of a function ^Béarla

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${\displaystyle v(y)/\|v(y)\|}$

symbol represents ^Béarla

unit vector ^Béarla

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proved by ^Béarla

Heinz Hopf

am

1926

1 reference

ráite i

Encyclopedia of Mathematics ^Béarla

URL tagartha

http://www.encyclopediaofmath.org/index.php/Poincaré-Hopf_theorem

teideal

Poincaré-Hopf theorem (Béarla)

á chothabháil ag WikiProject

WikiProject Mathematics ^Béarla

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Identifiers

Encyclopedia of Mathematics article ID ^Béarla

Poincaré-Hopf_theorem

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Freebase ID ^Béarla

/m/04nm34

1 reference

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Freebase Data Dumps ^Béarla

dáta foilsithe

28 Deireadh Fómhair 2013

Microsoft Academic ID ^Béarla

2780799127

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nLab ID ^Béarla

Poincaré–Hopf theorem

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Sitelinks

Vicipéid(11 entries)

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• cawiki Teorema de Poincaré-Hopf
• dewiki Satz von Poincaré-Hopf
• enwiki Poincaré–Hopf theorem
• frwiki Théorème de Poincaré-Hopf
• itwiki Teorema di Poincaré-Hopf
• jawiki ポアンカレ・ホップの定理
• kowiki 푸앵카레-호프 정리
• plwiki Twierdzenie Poincarégo-Hopfa
• ruwiki Теорема Пуанкаре о векторном поле
• ukwiki Теорема Пуанкаре про векторне поле
• zhwiki 庞加莱-霍普夫定理

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