Hello :) i am reading about knot theory especially torus links :) i read "Crossing number and Torus links" and the answer isn't clear. Does there exist a solution without topology but with group theory (the cyclic group $C_p$) or other proofs (combinatorics)? It is very difficult from my point of view -.- ... Thank you for help :)

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That question is about diagrams of knots. So the shortest route to an answer involves arguing about four-valent graphs in the plane. –  Sam Nead May 27 '13 at 9:01