Fred wrote: << On 10/20/09, Dan Asimov <dasimov@earthlink.net> wrote: << Linking is a fascinating phenomenon in topology, but the only chance of proving anything about it will require the use of a definition of linking.
Which is not supplied; although at a later stage (ex 5.8) a definition is requested! It turns out that for standard k-spheres, a simple and intuitive criterion is available.
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 _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele