We prove that the filtered GRID invariants of Legendrian links in link Floer homology, and consequently their associated invariants in the spectral sequence, obstruct decomposable Lagrangian cobordisms in the symplectization of the standard contact structure on ℝ3, strengthening a result by Baldwin, Lidman, and the fifth author.
J. A. Baldwin, T. Lidman, and C.-M. M. Wong. Lagrangian cobordisms and Legendrian invariants in knot Floer homology. Michigan Math. J., 71(1):145–175, 2022.
J. A. Baldwin and S. Sivek. Invariants of Legendrian and transverse knots in monopole knot homology. J. Symplectic Geom., 16(4):959–1000, 2018.
J. A. Baldwin and S. Sivek. On the equivalence of contact invariants in sutured Floer homology theories. Geom. Topol., 25(3):1087–1164, 2021.
F. Bourgeois and B. Chantraine. Bilinearized Legendrian contact homology and the augmentation category. J. Symplectic Geom., 12(3):553–583, 2014.
F. Bourgeois, J. M. Sabloff, and L. Traynor. Lagrangian cobordisms via generating families: construction and geography. Algebr. Geom. Topol., 15(4):2439–2477, 2015.
B. Chantraine. Lagrangian concordance of Legendrian knots. Algebr. Geom. Topol., 10(1):63–85, 2010.
B. Chantraine. A note on exact lagrangian cobordisms with disconnected legendrian ends. arXiv : Symplectic Geometry, pages 1325–1331, 2013.
B. Chantraine. Lagrangian concordance is not a symmetric relation. Quantum Topol., 6(3):451–474, 2015.
B. Chantraine, G. Dimitroglou Rizell, P. Ghiggini, and R. Golovko. Floer homology and Lagrangian concordance. In Proceedings of the Gökova Geometry-Topology Conference 2014, pages 76–113. Gökova Geometry/Topology Conference (GGT), Gökova, 2015.
Baptiste Chantraine. Some non-collarable slices of lagrangian surfaces. Bulletin of the London Mathematical Society, 44(5):981–987, April 2012.
Y. Chekanov. Differential algebra of Legendrian links. Invent. Math., 150(3):441–483, 2002.
W. Chongchitmate and L. Ng. An atlas of Legendrian knots. Exp. Math., 22(1):26–37, 2013.
Ch. Cornwell, L. Ng, and S. Sivek. Obstructions to Lagrangian concordance. Algebr. Geom. Topol., 16(2):797–824, 2016.
P. R. Cromwell. Embedding knots and links in an open book. I. Basic properties. Topology Appl., 64(1):37–58, 1995.
G. Dimitroglou Rizell. Legendrian ambient surgery and Legendrian contact homology. J. Symplectic Geom., 14(3):811–901, 2016.
G. Dimitroglou Rizell and R. Golovko. Instability of Legendrian knottedness, and non-regular Lagrangian concordances of knots. 2024.
T. Ekholm, Ko Honda, and T. Kálmán. Legendrian knots and exact Lagrangian cobordisms. J. Eur. Math. Soc. (JEMS), 18(11):2627–2689, 2016.
Y. Eliashberg, A. Givental, and H. Hofer. Introduction to symplectic field theory. Geom. Funct. Anal., Special Volume, Part II, pages 560–673, 2000.
M. Golla and A. Juhász. Functoriality of the EH class and the LOSS invariant under Lagrangian concordances. Algebr. Geom. Topol., 19(7):3683–3699, 2019.
Mitchell Jubeir, Ina Petkova, Noah Schwartz, Zachary Winkeler, and C.-M. Michael Wong. FilteredGRID. available at https://github.com/math-SHUR/FilteredGRID, 2024.
Ç. Kutluhan, G. Matić, J. Van Horn-Morris, and A. Wand. Filtering the Heegaard Floer contact invariant. Geom. Topol., 27(6):2181–2236, 2023.
C. Manolescu, P. Ozsváth, and S. Sarkar. A combinatorial description of knot Floer homo-logy. Ann. of Math. (2), 169(2):633–660, 2009.
C. Manolescu, P. Ozsváth, Z. Szabó, and D. Thurston. On combinatorial link Floer homo-logy. Geom. Topol., 11:2339–2412, 2007.
C. Manolescu, P. S. Ozsváth, and D. P. Thurston. Grid diagrams and Heegaard Floer invariants. 2024.
L. Meyers, R. Quarles, B. Roberts, D. Sh. Vela-Vick, and C.-M. M. Wong. transverse-hfk-revision. available at https://github.com/albenzo/transverse-hfk-revision/, 2019. accessed on Jun 7, 2019.
L. Ng, P. Ozsváth, and D. Thurston. TransverseHFK.c. available at https://services.math.duke.edu/~ng/math/TransverseHFK.c, 2007. accessed on Feb 8, 2019.
L. Ng, P. Ozsváth, and D. Thurston. Transverse knots distinguished by knot Floer homology. J. Symplectic Geom., 6(4):461–490, 2008.
P. Ozsváth, Z. Szabó, and D. Thurston. Legendrian knots, transverse knots and combinatorial Floer homology. Geom. Topol., 12(2):941–980, 2008.
P. S. Ozsváth, A. I. Stipsicz, and Z. Szabó. Grid homology for knots and links, volume 208 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2015.
Y. Pan. The augmentation category map induced by exact Lagrangian cobordisms. Algebr. Geom. Topol., 17(3):1813–1870, 2017.
J. M. Sabloff and L. Traynor. Obstructions to Lagrangian cobordisms between Legendrians via generating families. Algebr. Geom. Topol., 13(5):2733–2797, 2013.
D. Sauvaget. Curiosités lagrangiennes en dimension 4. Annales de l’institut Fourier, 54(6):1997–2020, 2004.
The Stacks project contributors. The Stacks project. available at https://stacks.math.columbia.edu, 2018. accessed on Jan 17, 2023.
Ch. A. Weibel. An introduction to homological algebra, volume 38 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1994.
C.-M. M. Wong. Grid diagrams and Manolescu’s unoriented skein exact triangle for knot Floer homology. Algebr. Geom. Topol., 17(3):1283–1321, 2017.
I. Zemke. Link cobordisms and functoriality in link Floer homology. J. Topol., 12(1):94–220, 2019.