Heegaard Floer homology and concordance bounds on the Thurston norm
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- by Daniele Celoria and Marco Golla; with an appendix with Adam Simon Levine PDF
- Trans. Amer. Math. Soc. 373 (2020), 295-318 Request permission
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.References
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Additional Information
- Daniele Celoria
- Affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom
- MR Author ID: 1153035
- Email: Daniele.Celoria@maths.ox.ac.uk
- Marco Golla
- Affiliation: CNRS, Laboratoire de Mathématiques Jean Leray, Université de Nantes, 44322 Nantes, France
- MR Author ID: 1098550
- Email: marco.golla@univ-nantes.fr
- Adam Simon Levine
- Affiliation: Duke University, 120 Science Drive, 117 Physics Building, Durham, North Carolina 27708
- MR Author ID: 849574
- ORCID: 0000-0002-9084-5124
- Email: alevine@math.duke.edu
- 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).
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 295-318
- MSC (2010): Primary 57M25, 57M26, 57M27
- DOI: https://doi.org/10.1090/tran/7906
- MathSciNet review: 4042876