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Transactions of the American Mathematical Society

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

 
 

 

Heegaard Floer homology and concordance bounds on the Thurston norm


Authors: Daniele Celoria and Marco Golla; with an appendix with Adam Simon Levine
Journal: Trans. Amer. Math. Soc. 373 (2020), 295-318
MSC (2010): Primary 57M25, 57M26, 57M27
DOI: https://doi.org/10.1090/tran/7906
Published electronically: September 12, 2019
MathSciNet review: 4042876
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Abstract: We prove that twisted correction terms in Heegaard Floer homology provide lower bounds on the Thurston norm of certain cohomology classes determined by the strong concordance class of a $ 2$-component link $ L$ in $ S^3$. We then specialise this procedure to knots in $ S^2 \times S^1$ and obtain a lower bound on their geometric winding number. We then provide an infinite family of null-homologous knots with increasing geometric winding number on which the bound is sharp.


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Additional Information

Daniele Celoria
Affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
Email: Daniele.Celoria@maths.ox.ac.uk

Marco Golla
Affiliation: CNRS, Laboratoire de Mathématiques Jean Leray, Université de Nantes, 44322 Nantes, France
Email: marco.golla@univ-nantes.fr

Adam Simon Levine
Affiliation: Duke University, 120 Science Drive, 117 Physics Building, Durham, North Carolina 27708
Email: alevine@math.duke.edu

DOI: https://doi.org/10.1090/tran/7906
Received by editor(s): July 12, 2018
Received by editor(s) in revised form: April 9, 2019, and May 18, 2019
Published electronically: September 12, 2019
Additional Notes: The authors acknowledge support from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No. 674978).
Article copyright: © Copyright 2019 American Mathematical Society