Finite extensions of local fields: Difference between revisions

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The '''Hopf theorem''' is a statement in [[differential topology]], saying that the [[degree of a continuous mapping|topological degree]] is the only [[homotopy invariant]] of [[continuous maps]] to [[n-sphere|sphere]]s.
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==Formal statement==
Let ''M'' be an ''n''-dimensional [[Closed manifold|compact]] [[Manifold#Orientability|oriented manifold]] and ''S''<sup>''n''</sup> the [[n-sphere|''n''-sphere]] and <math>f,g: M\to S^n</math> be continuous. Then <math>\deg(f)=\deg(g)</math> if and only if ''f'' and ''g'' are [[homotopic]].
 
==References==
* {{cite book|author=Milnor, J. W.|authorlink=John Milnor|title=Topology from the Differentiable Viewpoint|publisher=Princeton University Press|year=1997|isbn=978-0-691-04833-8}}
* {{cite book|author=Enrique Outerelo, Jesús M. Ruiz|title=Mapping degree theory|publisher=AMS|year=2009|isbn=978-0-8218-4915-6}}
 
{{Topology-stub}}
[[Category:Theorems in differential topology]]

Latest revision as of 02:21, 5 May 2014

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