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Winding number $ m$ and $ -m$ patterns acting on concordance


Author: Allison N. Miller
Journal: Proc. Amer. Math. Soc. 147 (2019), 2723-2731
MSC (2010): Primary 57M25, 57M27
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].


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Allison N. Miller
Affiliation: Department of Mathematics, Rice University, 6100 Main Street, Houston, Texas 77005

DOI: https://doi.org/10.1090/proc/14439
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
Article copyright: © Copyright 2019 American Mathematical Society