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After continuous deformation it is a regular 2d torus. I had trouble describing the situation in a clear way even though the picture...

Another way to think about the linking of two fibers in the Hopf fibration is to look at the topology of their complement in S^3. Take...

yes I just wanted to emphasiize that by sliding the linked pair of fibers along the rays emanating from the north pole of the three...

Here is a way of doing it using the Hopf fibration. Slide the two linked fibers along the rays emananting from the north pole of the 3...

Right. BTW: Your answer proves that the Klein bottle can be embedded in R^4. So for two linked fibers in 3 the 3 sphere, is the worry...

OK. So how would you move two linked loops in R^3 off of each other into R^4 without them crossing over each other? How would you move...

As an example, consider the equator of the three sphere, the circle in S^3 whose third and fourth coordinates are both zero. It divides...

What are your thoughts on this?

@Hornbein Intuitively, in Euclidean 3 space, two non-intersecting closed loops are linked if they cannot be separated without...

A way to construct topological manifolds from closed subsets of Euclidean space is through triangulations. For example, one can imagine...