“Slicing” the Hopf link

Krushkal, Vyacheslav

doi:10.2140/gt.2015.19.1657

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“Slicing” the Hopf link

Vyacheslav Krushkal

Geometry & Topology 19 (2015) 1657–1683

DOI: 10.2140/gt.2015.19.1657

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

Volume 19, issue 3 (2015)