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Aug 8, 2011 at 19:39 comment added André Henriques @ José: The fact that our two notions of "polynomial vector fields on $S^3$" agree is actually non-trivial. But this is indeed the case. The reason is the following: the variety $S^3_{\mathbb C}=\{(x,y,z,u)\in\mathbb C^4|x^2+y^2+z^2+u^2=1\}$ is isomorphic to the Lie group $SL(2,\mathbb C)=\{(a,b,c,d)\in\mathbb C^4|ad-bc=1\}$.
Aug 7, 2011 at 21:36 history answered José Figueroa-O'Farrill CC BY-SA 3.0