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A brief article on a brief proof. I'll be interested to see how well mathematicians that aren't topologists can grok the concepts described here.
@Ianagol
I did a grad degree in analytics and tool some grad courses in topology.
The article is not very good - I think I can reconstruct the definition of what kind of homotopy is allowed from the text, but the purpose of such an article is to give intuition: what kinds of knots are equivalent, examples of knots that dominate each other, etc. And maybe a word on what collections of equations are involved in the proof. (Are those geometric invariants? Topological invariants?)
@Pashhur I agree, it’s difficult to tell what the article is describing. What I used was the representation variety of the fundamental group of the knot complement (“knot group”) into a compact connected Lie group (like U(N) or SO(N)). I guess just defining these concepts was too much for an article of this scope. Knot groups have faithful representations into SO(N) for some N depending on the knot; I was aware of this from a mathoverflow question of Igor Belegradek.
@Ianagol Oh! I didn't realize you're the author of the proof! Congrats!