Covering link calculus and the bipolar filtration of topologically slice links

Cha, Jae Choon et Powell, Mark (2014). « Covering link calculus and the bipolar filtration of topologically slice links ». Geometry & Topology, 18(3), pp. 1539-1579.

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Résumé

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.

Type: Article de revue scientifique
Mots-clés ou Sujets: covering link calculus, concordance, bipolar filtration
Unité d'appartenance: Faculté des sciences > Département de mathématiques
Déposé par: Mark Powell
Date de dépôt: 19 avr. 2016 14:45
Dernière modification: 27 avr. 2016 18:28
Adresse URL : http://www.archipel.uqam.ca/id/eprint/8183

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