Some applications of Menke’s JSJ decomposition for symplectic fillings
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- by Austin Christian and Youlin Li;
- Trans. Amer. Math. Soc. 376 (2023), 4569-4604
- DOI: https://doi.org/10.1090/tran/8781
- Published electronically: April 19, 2023
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Abstract:
We apply Menke’s JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserving diffeomorphism of strong symplectic fillings of lens spaces. We show that exact symplectic fillings of contact manifolds obtained by surgery on certain Legendrian negative cables are the result of attaching a Weinstein 2-handle to an exact filling of a lens space. For large families of contact structures on Seifert fibered spaces over $S^2$, we reduce the problem of classifying exact symplectic fillings to the same problem for universally tight or canonical contact structures. Finally, virtually overtwisted circle bundles over surfaces with genus greater than one and negative twisting number are seen to have unique exact fillings.References
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Bibliographic Information
- Austin Christian
- Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia
- MR Author ID: 1427454
- ORCID: 0000-0001-8259-011X
- Youlin Li
- Affiliation: School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
- MR Author ID: 719542
- Received by editor(s): August 21, 2020
- Received by editor(s) in revised form: November 9, 2021, and July 1, 2022
- Published electronically: April 19, 2023
- Additional Notes: The first author was partially supported by NSF grant DMS-1745583. The second author was partially supported by Grants No. 11871332 and 12271349 of the National Natural Science Foundation of China.
- © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 376 (2023), 4569-4604
- MSC (2020): Primary 53D10; Secondary 53D05
- DOI: https://doi.org/10.1090/tran/8781
- MathSciNet review: 4608425