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

Powell, M. (2017) The four-genus of a link, Levine–Tristram signatures and satellites. Journal of Knot Theory and Its Ramifications, 26(2), 1740008. (doi: 10.1142/s0218216517400089)

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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-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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Powell, Dr Mark
Authors: Powell, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Knot Theory and Its Ramifications
Publisher:World Scientific Publishing
ISSN (Online):1793-6527
Published Online:21 November 2016
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