Geometry & Topology Volume 28, issue 3 (2024)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Symplectic capacities, unperturbed curves and convex toric domains

Dusa McDuff and Kyler Siegel

Geometry & Topology 28 (2024) 1213–1285

DOI: 10.2140/gt.2024.28.1213

Bibliography

1	F Bourgeois, A Morse–Bott approach to contact homology, from: "Symplectic and contact topology: interactions and perspectives" (editors Y Eliashberg, B Khesin, F Lalonde), Fields Inst. Commun. 35, Amer. Math. Soc. (2003) 55 MR1969267
2	F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799 MR2026549
3	F Bourgeois, K Mohnke, Coherent orientations in symplectic field theory, Math. Z. 248 (2004) 123 MR2092725
4	F Bourgeois, A Oancea, Symplectic homology, autonomous Hamiltonians, and Morse–Bott moduli spaces, Duke Math. J. 146 (2009) 71 MR2475400
5	J Chaidez, B Wormleighton, Lattice formulas for rational SFT capacities, preprint (2021) arXiv:2106.07920
6	K Choi, Combinatorial embedded contact homology for toric contact manifolds, preprint (2016) arXiv:1608.07988
7	K Cieliebak, K Mohnke, Symplectic hypersurfaces and transversality in Gromov–Witten theory, J. Symplectic Geom. 5 (2007) 281 MR2399678
8	K Cieliebak, K Mohnke, Punctured holomorphic curves and Lagrangian embeddings, Invent. Math. 212 (2018) 213 MR3773793
9	D Cristofaro-Gardiner, R Hind, Symplectic embeddings of products, Comment. Math. Helv. 93 (2018) 1 MR3777123
10	D Cristofaro-Gardiner, R Hind, D McDuff, The ghost stairs stabilize to sharp symplectic embedding obstructions, J. Topol. 11 (2018) 309 MR3789827
11	D Cristofaro-Gardiner, R Hind, K Siegel, Higher symplectic capacities and the stabilized embedding problem for integral elllipsoids [sic], J. Fixed Point Theory Appl. 24 (2022) 49 MR4439980
12	I Ekeland, H Hofer, Symplectic topology and Hamiltonian dynamics, Math. Z. 200 (1989) 355 MR0978597
13	I Ekeland, H Hofer, Symplectic topology and Hamiltonian dynamics, II, Math. Z. 203 (1990) 553 MR1044064
14	M Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR0809718
15	M Gromov, Soft and hard symplectic geometry, from: "Proceedings of the International Congress of Mathematicians, I" (editor A M Gleason), Amer. Math. Soc. (1987) 81 MR0934217
16	J Gutt, M Hutchings, Symplectic capacities from positive S¹–equivariant symplectic homology, Algebr. Geom. Topol. 18 (2018) 3537 MR3868228
17	R Hind, E Kerman, New obstructions to symplectic embeddings, Invent. Math. 196 (2014) 383 MR3193752
18	R K Hind, E Kerman, J–holomorphic cylinders between ellipsoids in dimension four, J. Symplectic Geom. 18 (2020) 1221 MR4174300
19	M Hutchings, The embedded contact homology index revisited, from: "New perspectives and challenges in symplectic field theory" (editors M Abreu, F Lalonde, L Polterovich), CRM Proc. Lecture Notes 49, Amer. Math. Soc. (2009) 263 MR2555941
20	M Hutchings, Quantitative embedded contact homology, J. Differential Geom. 88 (2011) 231 MR2838266
21	M Hutchings, Lecture notes on embedded contact homology, from: "Contact and symplectic topology" (editors F Bourgeois, V Colin, A Stipsicz), Bolyai Soc. Math. Stud. 26, Bolyai Math. Soc. (2014) 389 MR3220947
22	M Hutchings, Beyond ECH capacities, Geom. Topol. 20 (2016) 1085 MR3493100
23	M Hutchings, An elementary alternative to ECH capacities, Proc. Natl. Acad. Sci. USA 119 (2022)
24	M Hutchings, C H Taubes, Gluing pseudoholomorphic curves along branched covered cylinders, I, J. Symplectic Geom. 5 (2007) 43 MR2371184
25	M Hutchings, C H Taubes, Gluing pseudoholomorphic curves along branched covered cylinders, II, J. Symplectic Geom. 7 (2009) 29 MR2491716
26	D Irvine, The stabilized symplectic embedding problem for polydiscs, preprint (2019) arXiv:1907.13159
27	E Kerman, Y Liang, On symplectic capacities and their blind spots, J. Topol. Anal. (2023)
28	M Landry, M McMillan, E Tsukerman, On symplectic capacities of toric domains, Involve 8 (2015) 665 MR3366017
29	D McDuff, A remark on the stabilized symplectic embedding problem for ellipsoids, Eur. J. Math. 4 (2018) 356 MR3782228
30	D McDuff, K Siegel, Counting curves with local tangency constraints, J. Topol. 14 (2021) 1176 MR4332489
31	A Moreno, R Siefring, Holomorphic curves in the presence of holomorphic hypersurface foliations, preprint (2019) arXiv:1902.02700
32	J Pardon, Contact homology and virtual fundamental cycles, J. Amer. Math. Soc. 32 (2019) 825 MR3981989
33	M B Pereira, Equivariant symplectic homology, linearized contact homology and the Lagrangian capacity, PhD thesis, Universität Augsburg (2022) arXiv:2205.13381
34	M Schwarz, Morse homology, 111, Birkhäuser (1993) MR1239174
35	R Siefring, Intersection theory of punctured pseudoholomorphic curves, Geom. Topol. 15 (2011) 2351 MR2862160
36	K Siegel, Computing higher symplectic capacities, II, in preparation
37	K Siegel, Higher symplectic capacities, preprint (2019) arXiv:1902.01490
38	K Siegel, Computing higher symplectic capacities, I, Int. Math. Res. Not. 2022 (2022) 12402 MR4466005
39	C Wendl, Automatic transversality and orbifolds of punctured holomorphic curves in dimension four, Comment. Math. Helv. 85 (2010) 347 MR2595183
40	C Wendl, Lectures on symplectic field theory, lecture notes (2020)