Skip to main content

Research Repository

Advanced Search

Covering link calculus and the bipolar filtration of topologically slice links

Cha, Jae Choon; Powell, Mark

Covering link calculus and the bipolar filtration of topologically slice links Thumbnail


Authors

Jae Choon Cha

Mark Powell



Abstract

The bipolar filtration introduced by T Cochran, S Harvey and P Horn is a framework for the study of smooth concordance of topologically slice knots and links. It is known that there are topologically slice 1–bipolar knots which are not 2–bipolar. For knots, this is the highest known level at which the filtration does not stabilize. For the case of links with two or more components, we prove that the filtration does not stabilize at any level: for any n, there are topologically slice links which are n–bipolar but not (n + 1)–bipolar. In the proof we describe an explicit geometric construction which raises the bipolar height of certain links exactly by one. We show this using the covering link calculus. Furthermore we discover that the bipolar filtration of the group of topologically slice string links modulo smooth concordance has a rich algebraic structure.

Citation

Cha, J. C., & Powell, M. (2014). Covering link calculus and the bipolar filtration of topologically slice links. Geometry & Topology, 18(3), 1539-1579. https://doi.org/10.2140/gt.2014.18.1539

Journal Article Type Article
Acceptance Date Oct 7, 2013
Online Publication Date Jul 7, 2014
Publication Date Jul 7, 2014
Deposit Date Oct 3, 2017
Publicly Available Date Oct 3, 2017
Journal Geometry and Topology
Print ISSN 1465-3060
Electronic ISSN 1364-0380
Publisher Mathematical Sciences Publishers (MSP)
Peer Reviewed Peer Reviewed
Volume 18
Issue 3
Pages 1539-1579
DOI https://doi.org/10.2140/gt.2014.18.1539
Related Public URLs https://arxiv.org/abs/1212.5011

Files

Published Journal Article (556 Kb)
PDF

Copyright Statement
First published in Geometry & Topology in 18 (2014) 1539-1579, published by Mathematical Sciences Publishers. © 2014 Mathematical Sciences Publishers. All rights reserved.




You might also like



Downloadable Citations