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2015 “Slicing” the Hopf link
Vyacheslav Krushkal
Geom. Topol. 19(3): 1657-1683 (2015). DOI: 10.2140/gt.2015.19.1657


A link in the 3–sphere is called (smoothly) slice if its components bound disjoint smoothly embedded disks in the 4–ball. More generally, given a 4–manifold M with a distinguished circle in its boundary, a link in the 3–sphere is called M–slice if its components bound in the 4–ball disjoint embedded copies of M. A 4–manifold M is constructed such that the Borromean rings are not M–slice but the Hopf link is. This contrasts the classical link-slice setting where the Hopf link may be thought of as “the most nonslice” link. Further examples and an obstruction for a family of decompositions of the 4–ball are discussed in the context of the A-B slice problem.


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Vyacheslav Krushkal. "“Slicing” the Hopf link." Geom. Topol. 19 (3) 1657 - 1683, 2015.


Received: 25 February 2014; Revised: 5 August 2014; Accepted: 3 September 2014; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1321.57025
MathSciNet: MR3352246
Digital Object Identifier: 10.2140/gt.2015.19.1657

Primary: 57N13
Secondary: 57M25 , 57M27

Keywords: slice links , the A-B slice problem , the Milnor group

Rights: Copyright © 2015 Mathematical Sciences Publishers

Vol.19 • No. 3 • 2015
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