Any n-component link with linking number zero can be reduced to C_k-triviality in at most n^2 crossing changes, with a matching quadratic lower bound for some families, independent of k.
How many crossing changes or delta-moves does it take to get to a homotopy trivial link? 2025
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Gordian distance and clasper surgery for links
Any n-component link with linking number zero can be reduced to C_k-triviality in at most n^2 crossing changes, with a matching quadratic lower bound for some families, independent of k.