Degree of a Map: Directly Proving k is Degree of f

Thread starter wineesarne
Start date Aug 21, 2008
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Degree Map

Aug 21, 2008

wineesarne

Consider f: S¹ -> S¹: (cos 2 pi x, sin 2 pi x) -> (cos 2 k pi x, sin 2 k pi x).

How to show directly from the homological definition (without using Hurewicz etc) that degree(f) = k?

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Aug 21, 2008

NoMoreExams

Can you do something like this http://en.wikipedia.org/wiki/Degree_of_a_continuous_mapping#From_a_circle_to_itself

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