Doubly slice odd pretzel knots
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- by Clayton McDonald PDF
- Proc. Amer. Math. Soc. 148 (2020), 5413-5420 Request permission
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.References
- Andrew Donald, Embedding Seifert manifolds in $S^4$, Trans. Amer. Math. Soc. 367 (2015), no. 1, 559–595. MR 3271270, DOI 10.1090/S0002-9947-2014-06174-6
- Ahmad Issa and Duncan McCoy, Smoothly embedding Seifert fibered spaces in $S^4$, arXiv:1810.04770 2018.
- Martin Scharlemann, Smooth spheres in $\textbf {R}^4$ with four critical points are standard, Invent. Math. 79 (1985), no. 1, 125–141. MR 774532, DOI 10.1007/BF01388659
Additional Information
- Clayton McDonald
- Affiliation: Department of Mathematics, Boston College, 140 Commonwealth Avenue, Chestnut Hill, Massachusetts 02467
- Email: mcdonafi@bc.edu
- 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
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 5413-5420
- MSC (2010): Primary 57M25, 57M27, 57Q45
- DOI: https://doi.org/10.1090/proc/15022
- MathSciNet review: 4163852