A short proof of the Hairy Ball theorem (2016) [pdf]

Re:A short proof of the Hairy Ball theorem (2016) [pdf] by daynthelife on Tuesday August 26, 2025 @06:22AM (#45024587)

I am confused how we can define a rotation number of the map from S^1 to R^3 defined at the end of the second paragraph. R^3 is nullhomotopic, after all...

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Re:A short proof of the Hairy Ball theorem (2016) [pdf] by ajkjk on Tuesday August 26, 2025 @09:50AM (#45026558)

I think the idea is that you can't, but we're assuming v doesn't vanish at that point which would imply that it's possible?

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