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The four-genus of a link, Levine–Tristram signatures and satellites

Powell, Mark

The four-genus of a link, Levine–Tristram signatures and satellites Thumbnail


Authors

Mark Powell



Abstract

We give a new proof that the Levine–Tristram signatures of a link give lower bounds for the minimal sum of the genera of a collection of oriented, locally flat, disjointly embedded surfaces that the link can bound in the 4-ball. We call this minimal sum the 4-genus of the link. We also extend a theorem of Cochran, Friedl and Teichner to show that the 4-genus of a link does not increase under infection by a string link, which is a generalized satellite construction, provided that certain homotopy triviality conditions hold on the axis curves, and that enough Milnor's μ¯¯¯μ¯-invariants of the closure of the infection string link vanish. We construct knots for which the combination of the two results determines the 4-genus.

Citation

Powell, M. (2017). The four-genus of a link, Levine–Tristram signatures and satellites. Journal of Knot Theory and Its Ramifications, 26(02), Article 1740008. https://doi.org/10.1142/s0218216517400089

Journal Article Type Article
Acceptance Date May 22, 2016
Online Publication Date Nov 21, 2016
Publication Date Feb 1, 2017
Deposit Date Oct 3, 2017
Publicly Available Date Nov 21, 2017
Journal Journal of Knot Theory and Its Ramifications
Print ISSN 0218-2165
Electronic ISSN 1793-6527
Publisher World Scientific Publishing
Peer Reviewed Peer Reviewed
Volume 26
Issue 02
Article Number 1740008
DOI https://doi.org/10.1142/s0218216517400089
Related Public URLs https://arxiv.org/abs/1605.06833

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