Poincaré–Hopf theorem
id:
poincar-hopf-theorem-308-3763262
title:
Poincaré–Hopf theorem
text:
In mathematics, the Poincaré–Hopf theorem is an important theorem that is used in differential topology. It is named after Henri Poincaré and Heinz Hopf. The Poincaré–Hopf theorem is often illustrated by the special case of the hairy ball theorem, which simply states that there is no smooth vector field on an even-dimensional n-sphere having no sources or sinks.
brand slug:
wiki
category slug:
encyclopedia
description:
Counts 0s of a vector field on a differentiable manifold using its Euler characteristic
original url:
https://en.wikipedia.org/wiki/Poincar%C3%A9%E2%80%93Hopf_theorem
date created:
date modified:
2024-01-31T12:53:06Z
main entity:
{"identifier":"Q1305766","url":"https://www.wikidata.org/entity/Q1305766"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/a/a4/Poincare-Hopf.svg","width":512,"height":512}
fields total:
13
integrity:
15