Re: [math-fun] linked spheres

On 10/20/09, Dan Asimov <dasimov@earthlink.net> wrote:

... Yes. In fact, for disjoint round spheres S^p and S^q in R^n where p+q+1 = n, they link exactly when there exists a line L in R^n that intersects each sphere twice in alternating order.

(In other words, L intersects the spheres in two linked 0-spheres.)

--Dan

Completely different from the criterion I had in mind --- that they are not linked just when there exists a prime disjoint from and separating them! And Dan's criterion does yield an algorithm --- the line in question simply joins their centres. WFL