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Transactions of the American Mathematical Society

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Unlinking via simultaneous crossing changes

Author: Martin Scharlemann
Journal: Trans. Amer. Math. Soc. 336 (1993), 855-868
MSC: Primary 57M25
MathSciNet review: 1200011
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Abstract: Given two distinct crossings of a knot or link projection, we consider the question: Under what conditions can we obtain the unlink by changing both crossings simultaneously? More generally, for which simultaneous twistings at the crossings is the genus reduced? Though several examples show that the answer must be complicated, they also suggest the correct necessary conditions on the twisting numbers.

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Article copyright: © Copyright 1993 American Mathematical Society

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