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Is the sum of two functions from $S^n$ to $S^n$ an odd degree function?(I define the sum of them over its absolute value). Every odd function is of odd degree and the sum of two odd functions is odd but I don't know if this always holds for two functions of odd degree.

Bernard
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user297564
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  • Absolute value of what? If you are regarding $S^n$ as the unit sphere in $\mathbb R^{n+1}$, isn't the "absolute value" (I'm assuming you mean distance from origin) a constant $1$? – MPW Jul 02 '18 at 14:47
  • yes , but for sum of two functions it doesn't have to be 1, I think... – user297564 Jul 02 '18 at 14:48
  • It isn't clear what you mean then. It looks like you are using $|f|+|g|$, where $f$ and $g$ are maps $S^n\to S^n$. But then $|f|+|g|\equiv 1+1=2$. So please clarify, or at least give a simple example of such a "sum". – MPW Jul 02 '18 at 14:50
  • I mean f/|f+g| + g/|f+g| – user297564 Jul 02 '18 at 14:52
  • If the sum of two odd functions is odd, and every odd function is of odd degree, then of course the sum of two odd functions is of odd degree (as it is odd). – MPW Jul 02 '18 at 14:55
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    What does this have to do with topology? – Acccumulation Jul 02 '18 at 14:55
  • yes but I want to know if the sum of two functions of odd degree is odd – user297564 Jul 02 '18 at 15:07
  • I don't know if every function of odd defree is odd – user297564 Jul 02 '18 at 15:07
  • defenition of degree uses the n th homology group of $S^n$ . so I tagged algebraic topology.... – user297564 Jul 02 '18 at 15:09

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