#### Volume 19, issue 3 (2015)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts ISSN (electronic): 1364-0380 ISSN (print): 1465-3060

### 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 $M\phantom{\rule{0.3em}{0ex}}$–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 $M\phantom{\rule{0.3em}{0ex}}$–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