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