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Surface systems for links

Apparaît dans la collection : Knotted embeddings in dimensions 3 and 4 / Plongements noués en dimension 3 et 4

A surface system for a link in $S^3$ is a collection of embedded Seifert surfaces for the components, that are allowed to intersect one another. When do two $n$–component links with the same pairwise linking numbers admit homeomorphic surface systems? It turns out this holds if and only if the link exteriors are bordant over the free abelian group $\mathbb{Z}_n$. In this talk we characterise these geometric conditions in terms of algebraic link invariants in two ways: first the triple linking numbers and then the fundamental groups of the links. This involves a detailed study of the indeterminacy of Milnor’s triple linking numbers. Based on joint work with Chris Davis, Matthias Nagel and Patrick Orson.

Informations sur la vidéo

Date de captation 13/02/2018
Date de publication 18/02/2018
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19356803
Citer cette vidéo Powell, Mark (13/02/2018). Surface systems for links. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19356803
URL https://dx.doi.org/10.24350/CIRM.V.19356803

Domaine(s)

Topologie géométrique

Bibliographie

Davis, C.W., Nagel, M., Orson, P., & Powell, M. (2017). Triple linking numbers and surface systems. <arXiv:1709.08478> - https://arxiv.org/abs/1709.08478

Codes MSC

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