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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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-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 |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| 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: | 0218-2165 |
| ISSN (Online): | 1793-6527 |
| Published Online: | 21 November 2016 |
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