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Concordance to links with an unknotted component

Part of: Low-dimensional topology

Published online by Cambridge University Press:  07 October 2019

CHRISTOPHER W. DAVIS  and
JUNGHWAN PARK
CHRISTOPHER W. DAVIS
Affiliation:
Department of Mathematics, University of Wisconsin-Eau Claire, 533 Hibbard Hall, 124 Garfield Avenue, Eau Claire, WI 54701, U.S.A. e-mail: daviscw@uwec.edu
JUNGHWAN PARK
Affiliation:
School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160, U.S.A. e-mail: junghwan.park@math.gatech.edu
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Abstract

We construct links of arbitrarily many components each component of which is slice and yet are not concordant to any link with even one unknotted component. The only tool we use comes from the Alexander modules.

MSC classification

Primary: 57M25: Knots and links in $S^3$
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 170 , Issue 1 , January 2021 , pp. 155 - 160
Copyright
© Cambridge Philosophical Society 2019

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References

REFERENCES

[Bla57] Blanchfield, R. C.. Intersection theory of manifolds with operators with applications to knot theory. Ann. of Math. (2) 65 (1957), 340–356.10.2307/1969966CrossRefGoogle Scholar
[CO90] Cochran, T. D. and Orr, K. E.. Not all links are concordant to boundary links. Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 1, 99–106.10.1090/S0273-0979-1990-15912-9CrossRefGoogle Scholar
[CO93] Cochran, T. D. and Orr, K. E.. Not all links are concordant to boundary links. Ann. of Math. (2) 138 (1993), no. 3, 519–554.10.2307/2946555CrossRefGoogle Scholar
[Coc91] Cochran, T. D.. k-cobordism for links in S 3. Trans. Amer. Math. Soc. 327 (1991), no. 2, 641–654.Google Scholar
[CR12] Cha, J. C. and Ruberman, D.. Concordance to links with unknotted components. Algebr. Geom. Topol. 12 (2012), no. 2, 963–977.10.2140/agt.2012.12.963CrossRefGoogle Scholar
[Fri] Friedl, S.. Concordance of links and their components.Google Scholar
[HLL18] Hom, J., Levine, A. S. and Lidman, T.. Knot concordance in homology cobordisms (2018).Google Scholar
[Kea75] Kearton, C.. Cobordism of knots and Blanchfield duality. J. London Math. Soc. (2) 10 (1975), no. 4, 406–408.10.1112/jlms/s2-10.4.406CrossRefGoogle Scholar
[Lev16] Levine, A. S.. Nonsurjective satellite operators and piecewise-linear concordance. Forum Math. Sigma 4 (2016), e34, 47.10.1017/fms.2016.31CrossRefGoogle Scholar
[Liv90] Livingston, C.. Links not concordant to boundary links. Proc. Amer. Math. Soc. 110 (1990), no. 4, 1129–1131.Google Scholar