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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

   
 
 

 

On the topological 4-genus of torus knots


Authors: S. Baader, P. Feller, L. Lewark and L. Liechti
Journal: Trans. Amer. Math. Soc. 370 (2018), 2639-2656
MSC (2010): Primary 57M25
DOI: https://doi.org/10.1090/tran/7051
Published electronically: December 19, 2017
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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.


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Additional Information

S. Baader
Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
Email: sebastian.baader@math.unibe.ch

P. Feller
Affiliation: Department of Mathematics, Boston College, Maloney Hall, Chestnut Hill, Massachusetts 02467
Address at time of publication: ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
Email: peter.feller@math.ch

L. Lewark
Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
Email: lukas.lewark@math.unibe.ch

L. Liechti
Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
Email: livio.liechti@math.unibe.ch

DOI: https://doi.org/10.1090/tran/7051
Received by editor(s): October 19, 2015
Received by editor(s) in revised form: June 20, 2016, and August 2, 2016
Published electronically: December 19, 2017
Additional Notes: The third author thanks the EPSRC grant EP/K00591X/1 for providing computing facilities
The second, third and fourth authors gratefully acknowledge support by the SNSF grants 155477 and 159208, respectively
Article copyright: © Copyright 2017 by the authors

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