Suppose I sit in R^4 with a single 2-sphere, x^2+y^2+z^2=1, and an infinite number of circles of radius one that are free to move in R^4. Is it true that one can arrange these infinite number of circles so that their union is the three-sphere S^3, defined by x^2+y^2+z^2+w^2=1 and each circle is disjoint from all other circles but intersects the 2-sphere at one point? Is this a Hopf fibration?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks for any help!

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# Constructing S^3 from a S^2 and a bunch of S^1's?

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