A non-degenerate exchange move on a closed n-braid always yields infinitely many non-conjugate n-braid representatives of the same link.
Stoimenow, Non-conjugate braids with the same closure link from density of representations, J
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A non-degenerate exchange move always produces infinitely many non-conjugate braids
A non-degenerate exchange move on a closed n-braid always yields infinitely many non-conjugate n-braid representatives of the same link.