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Triple linking numbers and surface systems

Davis, Christopher William; Nagel, Matthias; Orson, Patrick; Powell, Mark

Authors

Christopher William Davis

Matthias Nagel

Patrick Orson

Mark Powell



Abstract

We give a refined value group for the collection of triple linking numbers of links in the 3–sphere. Given two links with the same pairwise linking numbers we show that they have the same refined triple linking number collection if and only if the links admit homeomorphic surface systems. Moreover these two conditions hold if and only if the link exteriors are bordant over BZ n, and if and only if the third lower central series quotients π/π3 of the link groups are isomorphic preserving meridians and longitudes. We also show that these conditions imply that the link groups have isomorphic fourth lower central series quotients π/π4, preserving meridians.

Citation

Davis, C. W., Nagel, M., Orson, P., & Powell, M. (2020). Triple linking numbers and surface systems. Indiana University Mathematics Journal, 69(7), 2505-2547. https://doi.org/10.1512/iumj.2020.69.8081

Journal Article Type Article
Acceptance Date May 28, 2019
Online Publication Date Mar 4, 2020
Publication Date Jan 1, 2020
Deposit Date May 28, 2019
Publicly Available Date Mar 28, 2024
Journal Indiana University Mathematics Journal
Print ISSN 0022-2518
Electronic ISSN 1943-5258
Publisher Indiana University Mathematics Journal
Peer Reviewed Peer Reviewed
Volume 69
Issue 7
Pages 2505-2547
DOI https://doi.org/10.1512/iumj.2020.69.8081
Publisher URL https://www.iumj.indiana.edu/IUMJ/Preprints/8081.pdf
Related Public URLs https://arxiv.org/abs/1709.08478

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