Winding number $m$ and $-m$ patterns acting on concordance
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- by Allison N. Miller
- Proc. Amer. Math. Soc. 147 (2019), 2723-2731
- DOI: https://doi.org/10.1090/proc/14439
- Published electronically: March 7, 2019
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Abstract:
We prove that for any winding number $m>0$ pattern $P$ and winding number $-m$ pattern $Q$, there exist knots $K$ such that the minimal genus of a cobordism between $P(K)$ and $Q(K)$ is arbitrarily large. This answers a question posed by Cochran-Harvey [Algebr. Geom. Topol. 18 (2018), pp. 2509–2540] and generalizes a result of Kim-Livingston [Pacific J. Math. 220 (2005), pp. 87–105].References
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Bibliographic Information
- Allison N. Miller
- Affiliation: Department of Mathematics, Rice University, 6100 Main Street, Houston, Texas 77005
- MR Author ID: 999009
- Received by editor(s): January 17, 2018
- Received by editor(s) in revised form: September 23, 2018
- Published electronically: March 7, 2019
- Communicated by: David Futer
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 2723-2731
- MSC (2010): Primary 57M25, 57M27
- DOI: https://doi.org/10.1090/proc/14439
- MathSciNet review: 3951445