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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.

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

Concordance of Bing Doubles and Boundary Genus†

  • DOI:
  • Published online: 18 July 2011

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.

[2]S. Cappell and J. Shaneson Link cobordism. Comment. Math. Helv. 55 (1980), 2049.

[5]J. C. Cha and T. Kim Covering link calculus and iterated Bing doubles. Geom. Topol. 12 (2008), 21732201.

[7]D. Cimasoni Slicing Bing doubles. Algebr. Geom. Topol. 6 (2006), 23952415.

[8]T. Cochran , S. Harvey and C. Leidy Link concordance and generalized doubling operators. Algebr. Geom. Topology 8 (2008), 15931646.

[9]T. Cochran and K. Orr Not all links are concordant to boundary links. Ann. of Math. (2) 138 (1993), 519554.

[10]P. Conner and E. Floyd Differentiable periodic maps. Ergeb. Math. Grenzgeb., N. F., Band 33 (Academic Press Inc., Springer-Verlag, 1964).

[13]P. Gilmer and C. Livingston The Casson-Gordon invariant and link concordance. Topology 31 (1992), 475492.

[14]S. Harvey Homology cobordism invariants and the Cochran–Orr–Teichner filtration of the link concordance group. Geom. Topol. 12 (2008), 387430.

[16]J. Levine Invariants of knot cobordism. Invent. Math. 8 (1969), 98110.

[17]J. Levine Link invariants via the eta invariant. Comment. Math. Helv. 69 (1994), 82119.

[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.

[21]H. Murakami and A. Yasuhara Four-genus and four-dimensional clasp number of a knot, Proc. Amer. Math. Soc. 128 (2000), 36933699.

[22]K. Murasugi On a certain numerical invariant of link types. Trans. Amer. Math. Soc. 117 (1965), 387422.

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

[24]O. Plamenevskaya Bounds for Thurston-Bennequin number from Floer homology. Algebr. Geom. Topol. 4 (2004), 399406.

[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
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  • EISSN: 1469-8064
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