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Given a map $f:B^n \to S^n$, where $B^n$ is the unit ball and $S^n$ is the unit sphere, is it true that the degree of $f|_{S^n}$ is always 0, where $f_{S^n}$ is the restriction of $f$ to $S^n$? If so, why?

Thanks!

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    Do you perhaps want that $f$ is continuous? And also, just by way of clarification: is $S^n$ the boundary of $B^n$ (I personally would write it $S^{n-1}$, but it is just a matter of convention...)2011-01-03
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    Yes for both questions,2011-01-03
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    It's not *just* convention, the superscripts denote the dimension of the manifold! Which makes it really, really confusing to write anything besides $\partial(B^n)=S^{n-1}$...2011-01-04

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