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AbstractFor any pair of knots of Gordian distance two, we construct an infinite family of knots which are between these two knots, that is, which differ from the given two knots by one crossing change. In particular, we prove that every knot of unknotting number two can be unknotted via infinitely many different knots of unknotting number one.
The Quarterly Journal of Mathematics – Oxford University Press
Published: Jun 17, 2006
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