On Floer minimal knots in sutured manifolds
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- by Zhenkun Li, Yi Xie and Boyu Zhang HTML | PDF
- Trans. Amer. Math. Soc. Ser. B 9 (2022), 499-516
Abstract:
Suppose $(M, \gamma )$ is a balanced sutured manifold and $K$ is a rationally null-homologous knot in $M$. It is known that the rank of the sutured Floer homology of $M\backslash N(K)$ is at least twice the rank of the sutured Floer homology of $M$. This paper studies the properties of $K$ when the equality is achieved for instanton homology. As an application, we show that if $L\subset S^3$ is a fixed link and $K$ is a knot in the complement of $L$, then the instanton link Floer homology of $L\cup K$ achieves the minimum rank if and only if $K$ is the unknot in $S^3\backslash L$.References
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Additional Information
- Zhenkun Li
- Affiliation: Department of Mathematics, Stanford University, California 94305
- MR Author ID: 1252899
- ORCID: 0000-0002-0217-4173
- Email: zhenkun@stanford.edu
- Yi Xie
- Affiliation: Beijing International Center for Mathematical Research, Peking University, Beijing 100871, People’s Republic of China
- ORCID: 0000-0001-8857-4284
- Email: yixie@pku.edu.cn
- Boyu Zhang
- Affiliation: Department of Mathematics, Princeton University, New Jersey 08544
- MR Author ID: 1284956
- ORCID: 0000-0001-8012-9311
- Email: bz@math.princeton.edu
- Received by editor(s): August 30, 2021
- Received by editor(s) in revised form: November 13, 2021, and November 15, 2021
- Published electronically: June 1, 2022
- Additional Notes: The second author was supported by National Key R&D Program of China SQ2020YFA0712800 and NSFC 12071005.
- © Copyright 2022 by the authors under Creative Commons Attribution-NonCommercial 3.0 License (CC BY NC 3.0)
- Journal: Trans. Amer. Math. Soc. Ser. B 9 (2022), 499-516
- MSC (2020): Primary 57K18
- DOI: https://doi.org/10.1090/btran/105
- MathSciNet review: 4432446