Computing the unknotting numbers of certain pretzel knots

Seph Shewell Brockway

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arXiv · 1312.4502

Computing the unknotting numbers of certain pretzel knots

Seph Shewell Brockway

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Abstract

We compute the unknotting number of two infinite families of pretzel knots, $P(3,1,\dots,1,b)$ (with $b$ positive and odd and an odd number of 1s) and $P(3,3,3c)$ (with $c$ positive and odd). To do this, we extend a technique of Owens using Donaldson's diagonalization theorem, and one of Traczyk using the Jones polynomial, building on work of Lickorish and Millett.

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BibTeX RIS

Seph Shewell Brockway. 2013-12-16. Computing the unknotting numbers of certain pretzel knots. https://arxiv.org/abs/1312.4502

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