On the topological 4-genus of torus knots-Reference-Cited by-同舟云学术

On the topological 4-genus of torus knots

Published:2017-12-19 Issue:4 Volume:370 Page:2639-2656
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Baader S.,Feller P.,Lewark L.,Liechti L.

Abstract

We prove that the topological locally flat slice genus of large torus knots takes up less than three quarters of the ordinary genus. As an application, we derive the best possible linear estimate of the topological slice genus for torus knots with non-maximal signature invariant.

Funder

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/tran/2018-370-04/S0002-9947-2017-07051-3/tran7051_AM.pdf

Reference23 articles.

1. Scissor equivalence for torus links;Baader, Sebastian;Bull. Lond. Math. Soc.,2012

2. [BL15] Sebastian Baader and Lukas Lewark: The stable 4-genus of alternating knots, 2015, to appear in Asian J. Math. arXiv:1505.03345.

3. [Col15] J. Collins, Seifert matrix computation, retrieved 2015. A computer program to compute Seifert matrices from braids, available from \url{http://www.maths.ed.ac.uk/ jcollins/SeifertMatrix/}.

4. Princeton Mathematical Series;Farb, Benson,2012

5. The degree of the Alexander polynomial is an upper bound for the topological slice genus;Feller, Peter;Geom. Topol.,2016

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