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NOTE ON CROSSING CHANGES

NOTE ON CROSSING CHANGES 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Quarterly Journal of Mathematics Oxford University Press

NOTE ON CROSSING CHANGES

The Quarterly Journal of Mathematics , Volume 57 (2) – Jun 17, 2006

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References (8)

Publisher
Oxford University Press
Copyright
© Published by Oxford University Press.
ISSN
0033-5606
eISSN
1464-3847
DOI
10.1093/qmath/hai010
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

The Quarterly Journal of MathematicsOxford University Press

Published: Jun 17, 2006

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