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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
“Slicing” the Hopf link

Vyacheslav Krushkal

Geometry & Topology 19 (2015) 1657–1683
Abstract

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.

Keywords
Slice links, the Milnor group, the A-B slice problem
Mathematical Subject Classification 2010
Primary: 57N13
Secondary: 57M25, 57M27
References
Publication
Received: 25 February 2014
Revised: 5 August 2014
Accepted: 3 September 2014
Published: 21 May 2015
Proposed: Robion Kirby
Seconded: Michael Freedman, Walter Neumann
Authors
Vyacheslav Krushkal
Department of Mathematics
University of Virginia
Charlottesville, VA 22904
USA
http://www.math.virginia.edu/~vk6e