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  • Cited by 3
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Kim, Se-Goo and Yeon, Mi Jeong 2015. Rasmussen and Ozsváth–Szabó invariants of a family of general pretzel knots. Journal of Knot Theory and Its Ramifications, Vol. 24, Issue. 03, p. 1550017.


    Cha, Jae Choon and Powell, Mark 2014. Covering link calculus and the bipolar filtration of topologically slice links. Geometry & Topology, Vol. 18, Issue. 3, p. 1539.


    VAN COTT, CORNELIA A. 2013. AN OBSTRUCTION TO SLICING ITERATED BING DOUBLES. Journal of Knot Theory and Its Ramifications, Vol. 22, Issue. 06, p. 1350029.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 151, Issue 3
  • November 2011, pp. 459-470

Concordance of Bing Doubles and Boundary Genus†

  • CHARLES LIVINGSTON (a1) and CORNELIA A. VAN COTT (a2)
  • DOI: http://dx.doi.org/10.1017/S0305004111000442
  • Published online: 18 July 2011
Abstract
Abstract

Cha and Kim proved that if a knot K is not algebraically slice, then no iterated Bing double of K is concordant to the unlink. We prove that if K has nontrivial signature σ, then the n–iterated Bing double of K is not concordant to any boundary link with boundary surfaces of genus less than 2n−1σ. The same result holds with σ replaced by 2τ, twice the Ozsváth–Szabó knot concordance invariant.

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[1]R. H. Bing A homeomorphism between the 3-sphere and the sum of two solid horned spheres. Ann. of Math. (2) 56 (1952), 354362.

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[19]C. Livingston Links not concordant to boundary links. Proc. Amer. Math. Soc. 110 (1990), 11291131.

[20]C. Livingston Computations of the Ozsváth–Szabó knot concordance invariant. Geom. Topol. 8 (2004), 735742.

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[23]P. Ozsváth and Z. Szabó Knot Floer homology and the four-ball genus. Geom. Topol. 7 (2003), 615639.

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[25]J. Rasmussen Khovanov homology and the slice genus. Invent. math. 182 (2010), 419447.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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