Algebraic & Geometric Topology

Slicing Bing doubles

David Cimasoni

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796641

Digital Object Identifier
doi:10.2140/agt.2006.6.2395

Mathematical Reviews number (MathSciNet)
MR2286030

Zentralblatt MATH identifier
1129.57007

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

Keywords
Bing double slice link boundary link Rasmussen invariant

Citation

Cimasoni, David. Slicing Bing doubles. Algebr. Geom. Topol. 6 (2006), no. 5, 2395--2415. doi:10.2140/agt.2006.6.2395. https://projecteuclid.org/euclid.agt/1513796641


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