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Doubly slice odd pretzel knots


Author: Clayton McDonald
Journal: Proc. Amer. Math. Soc. 148 (2020), 5413-5420
MSC (2010): Primary 57M25, 57M27, 57Q45
DOI: https://doi.org/10.1090/proc/15022
Published electronically: September 18, 2020
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Abstract: We prove that an odd pretzel knot is doubly slice if it has $ 2n+1$ twist parameters consisting of $ n+1$ copies of $ a$ and $ n$ copies of $ -a$ for some odd integer $ a$. Combined with the work of Issa and McCoy, it follows that these are the only doubly slice odd pretzel knots.


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Additional Information

Clayton McDonald
Affiliation: Department of Mathematics, Boston College, 140 Commonwealth Avenue, Chestnut Hill, Massachusetts 02467
Email: mcdonafi@bc.edu

DOI: https://doi.org/10.1090/proc/15022
Received by editor(s): October 22, 2019
Received by editor(s) in revised form: January 7, 2020, January 10, 2020, and January 12, 2020
Published electronically: September 18, 2020
Communicated by: David Futer
Article copyright: © Copyright 2020 American Mathematical Society