Surface systems and triple linking numbers

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

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We characterise when two links in the 3–sphere admit homeomorphic surface systems, where a surface system is a collection of embedded surfaces with boundary the link. The answer is in terms of 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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Powell, Dr Mark
Authors: Davis, C. W., Nagel, M., Orson, P., and Powell, M.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Indiana University Mathematics Journal
Journal Abbr.:Indiana Univ. Math. J.
Publisher:Indiana University Mathematics Journal
ISSN (Online):1943-5258
Published Online:04 March 2020
Copyright Holders:Copyright © 2020 Indiana University Mathematics Journal
First Published:First published in Indiana University Mathematics Journal 69(7): 2505-2547
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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