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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Links with non-trivial Alexander polynomial which are topologically concordant to the Hopf link


Authors: Min Hoon Kim, David Krcatovich and JungHwan Park
Journal: Trans. Amer. Math. Soc. 371 (2019), 5379-5400
MSC (2010): Primary 20J05, 57M07; Secondary 55P60, 57M27
DOI: https://doi.org/10.1090/tran/7389
Published electronically: January 15, 2019
MathSciNet review: 3937296
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Abstract: We give infinitely many 2-component links with unknotted components which are topologically concordant to the Hopf link, but not smoothly concordant to any 2-component link with trivial Alexander polynomial. Our examples are pairwise non-concordant.


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Additional Information

Min Hoon Kim
Affiliation: School of Mathematics, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
MR Author ID: 1067137
Email: kminhoon@kias.re.kr

David Krcatovich
Affiliation: Department of Mathematics, Rice University, 6100 Main Street, Houston, Texas 77005
MR Author ID: 1128670
Email: dk27@rice.edu

JungHwan Park
Affiliation: Department of Mathematics, Rice University, 6100 Main Street, Houston, Texas 77005
MR Author ID: 1188099
Email: jp35@rice.edu

Keywords: Link concordance, Heegaard Floer homology, Correction term, Hopf link, Alexander polynomial
Received by editor(s): April 5, 2017
Received by editor(s) in revised form: August 17, 2017, and September 6, 2017
Published electronically: January 15, 2019
Additional Notes: The first author was partially supported by the Overseas Research Program for Young Scientists through the Korea Institute for Advanced Study.
The third author was partially supported by the National Science Foundation grant DMS-1309081.
The first and the third authors thank the Hausdorff Institute for Mathematics in Bonn for both support and its outstanding research environment.
Article copyright: © Copyright 2019 American Mathematical Society