Knotted embeddings in dimensions 3 and 4 / Plongements noués en dimension 3 et 4

Collection Knotted embeddings in dimensions 3 and 4 / Plongements noués en dimension 3 et 4

Organizer(s) Audoux, Benjamin ; Baader, Sebastian ; Lecuona, Ana G.

Date(s) 12/02/2018 - 16/02/2018

linked URL https://conferences.cirm-math.fr/1893.html

00:00:00 / 00:00:00

3 5

Surface systems for links

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.

Information about the video

Date of recording 13/02/2018
Date of publication 18/02/2018
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19356803
Cite this video 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

Domain(s)

Geometric Topology

Bibliography

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

MSC codes

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