Algebraic & Geometric Topology

Slicing Bing doubles

David Cimasoni

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Bing doubling is an operation which produces a 2–component boundary link B(K) from a knot K. If K is slice, then B(K) is easily seen to be boundary slice. In this paper, we investigate whether the converse holds. Our main result is that if B(K) is boundary slice, then K is algebraically slice. We also show that the Rasmussen invariant can tell that certain Bing doubles are not smoothly slice.

Article information

Algebr. Geom. Topol., Volume 6, Number 5 (2006), 2395-2415.

Received: 16 September 2006
Accepted: 18 November 2006
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

Bing double slice link boundary link Rasmussen invariant


Cimasoni, David. Slicing Bing doubles. Algebr. Geom. Topol. 6 (2006), no. 5, 2395--2415. doi:10.2140/agt.2006.6.2395.

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  • A Beliakova, S Wehrli, Categorification of the colored Jones polynomial and Rasmussen invariant of links
  • R H Bing, }, Ann. of Math. $(2)$ 56 (1952) 354–362
  • R Budney, JSJ-decompositions of knot and link complements in the 3-sphere
  • J C Cha, K H Ko, Signature invariants of links from irregular covers and non-abelian covers, Math. Proc. Cambridge Philos. Soc. 127 (1999) 67–81
  • D Cimasoni, V Florens, Generalized Seifert surfaces and signatures of colored links
  • D Cooper, The universal abelian cover of a link, from: “Low-dimensional topology (Bangor, 1979)”, London Math. Soc. Lecture Note Ser. 48, Cambridge Univ. Press, Cambridge (1982) 51–66
  • M H Freedman, F Quinn, Topology of 4-manifolds, Princeton Mathematical Series 39, Princeton University Press
  • S Friedl, Link concordance, boundary link concordance and eta-invariants, Math. Proc. Cambridge Philos. Soc. 138 (2005) 437–460
  • S Harvey, Homology cobordism invariants and the Cochran-Orr-Teichner filtration of the link concordance group
  • A Hatcher, Basic Topology of 3-Manifolds Available at \setbox0\makeatletter\@url {\unhbox0
  • A Kawauchi, On the Alexander polynomials of cobordant links, Osaka J. Math. 15 (1978) 151–159
  • K H Ko, private communication
  • K H Ko, 869227
  • C Livingston, Computations of the Ozsváth-Szabó knot concordance invariant, Geom. Topol. 8 (2004) 735–742
  • C Livingston, S Naik, Ozsváth-Szabó and Rasmussen invariants of doubled knots, Algebr. Geom. Topol. 6 (2006) 651–657
  • K Murasugi, On the Arf invariant of links, Math. Proc. Cambridge Philos. Soc. 95 (1984) 61–69
  • J Rasmussen, Khovanov homology and the slice genus
  • L Rudolph, Quasipositivity as an obstruction to sliceness, Bull. Amer. Math. Soc. $($N.S.$)$ 29 (1993) 51–59
  • L Rudolph, An obstruction to sliceness via contact geometry and “classical” gauge theory, Invent. Math. 119 (1995) 155–163
  • D Sheiham, Invariants of boundary link cobordism, Mem. Amer. Math. Soc. 165 (2003) x+110
  • A Shumakovitch, Rasmussen invariant, Slice-Bennequin inequality, and sliceness of knots
  • P Teichner, private communication