Geometry & Topology Volume 29, issue 7 (2025)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

A landscape of contact manifolds via rational SFT

Agustin Moreno and Zhengyi Zhou

Geometry & Topology 29 (2025) 3465–3565

DOI: 10.2140/gt.2025.29.3465

Bibliography

1	C Abbas, K Cieliebak, H Hofer, The Weinstein conjecture for planar contact structures in dimension three, Comment. Math. Helv. 80 (2005) 771 MR2182700
2	B Acu, The Weinstein conjecture for iterated planar contact structures, preprint (2017) arXiv:1710.07724
3	B Acu, O Capovilla-Searle, A Gadbled, A Marinković, E Murphy, L Starkston, A Wu, An introduction to Weinstein handlebodies for complements of smoothed toric divisors, from: "Research directions in symplectic and contact geometry and topology" (editors B Acu, C Cannizzo, D McDuff, Z Myer, Y Pan, L Traynor), Assoc. Women Math. Ser. 27, Springer ([2021] ©2021) 217 MR4417717
4	B Acu, J B Etnyre, B Ozbagci, Generalizations of planar contact manifolds to higher dimensions, J. Symplectic Geom. 21 (2023) 683 MR4687585
5	B Acu, A Moreno, Planarity in higher-dimensional contact manifolds, Int. Math. Res. Not. 2022 (2022) 4222 MR4391886
6	E Bao, K Honda, Semi-global Kuranishi charts and the definition of contact homology, Adv. Math. 414 (2023) 108864 MR4539062
7	M S Borman, Y Eliashberg, E Murphy, Existence and classification of overtwisted contact structures in all dimensions, Acta Math. 215 (2015) 281 MR3455235
8	F Bourgeois, A Morse–Bott approach to contact homology, PhD thesis, Stanford University (2002) MR2703292
9	F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799 MR2026549
10	F Bourgeois, O van Koert, Contact homology of left-handed stabilizations and plumbing of open books, Commun. Contemp. Math. 12 (2010) 223 MR2646902
11	F Bourgeois, K Mohnke, Coherent orientations in symplectic field theory, Math. Z. 248 (2004) 123 MR2092725
12	F Bourgeois, K Niederkrüger, Towards a good definition of algebraically overtwisted, Expo. Math. 28 (2010) 85 MR2606237
13	F Bourgeois, A Oancea, An exact sequence for contact- and symplectic homology, Invent. Math. 175 (2009) 611 MR2471597
14	F Bourgeois, A Oancea, Symplectic homology, autonomous Hamiltonians, and Morse–Bott moduli spaces, Duke Math. J. 146 (2009) 71 MR2475400
15	F Bourgeois, A Oancea, Erratum to : An exact sequence for contact- and symplectic homology [2471597], Invent. Math. 200 (2015) 1065 MR3348144
16	F Bourgeois, A Oancea, S¹-equivariant symplectic homology and linearized contact homology, Int. Math. Res. Not. 2017 (2017) 3849 MR3671507
17	J Bowden, D Crowley, A I Stipsicz, The topology of Stein fillable manifolds in high dimensions, I, Proc. Lond. Math. Soc. 109 (2014) 1363 MR3293153
18	J Bowden, D Crowley, A I Stipsicz, The topology of Stein fillable manifolds in high dimensions, II, Geom. Topol. 19 (2015) 2995 MR3416120
19	J Bowden, F Gironella, A Moreno, Bourgeois contact structures: tightness, fillability and applications, Invent. Math. 230 (2022) 713 MR4493326
20	K Cieliebak, Y Eliashberg, From Stein to Weinstein and back : symplectic geometry of affine complex manifolds, 59, Amer. Math. Soc. (2012) MR3012475
21	K Cieliebak, K Fukaya, J Latschev, Homological algebra related to surfaces with boundary, Quantum Topol. 11 (2020) 691 MR4191652
22	K Cieliebak, J Latschev, The role of string topology in symplectic field theory, 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) 113 MR2555935
23	K Cieliebak, K Mohnke, Punctured holomorphic curves and Lagrangian embeddings, Invent. Math. 212 (2018) 213 MR3773793
24	J Conway, J B Etnyre, Contact surgery and symplectic caps, Bull. Lond. Math. Soc. 52 (2020) 379 MR4171373
25	S Courte, Contact manifolds with symplectomorphic symplectizations, Geom. Topol. 18 (2014) 1 MR3158770
26	F Ding, H Geiges, E₈-plumbings and exotic contact structures on spheres, Int. Math. Res. Not. 2004 (2004) 3825 MR2104476
27	L Diogo, S T Lisi, Symplectic homology of complements of smooth divisors, J. Topol. 12 (2019) 967 MR4072162
28	Y Eliashberg, Classification of overtwisted contact structures on 3-manifolds, Invent. Math. 98 (1989) 623 MR1022310
29	Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, Geom. Funct. Anal. GAFA 2000 special volume (2000) 560 MR1826267
30	Y Eliashberg, E Murphy, Making cobordisms symplectic, J. Amer. Math. Soc. 36 (2023) 1 MR4495837
31	J B Etnyre, Planar open book decompositions and contact structures, Int. Math. Res. Not. 2004 (2004) 4255 MR2126827
32	J B Etnyre, K Honda, On symplectic cobordisms, Math. Ann. 323 (2002) 31 MR1906906
33	J Fish, H Hofer, Applications of polyfold theory, II : The polyfolds of symplectic field theory, in preparation
34	J W Fish, H Hofer, Lectures on polyfolds and symplectic field theory, preprint (2018) arXiv:1808.07147
35	S Ganatra, D Pomerleano, Symplectic cohomology rings of affine varieties in the topological limit, Geom. Funct. Anal. 30 (2020) 334 MR4108612
36	S Ganatra, K Siegel, On the embedding complexity of Liouville manifolds, J. Differential Geom. 127 (2024) 1019 MR4773173
37	A Gathmann, Absolute and relative Gromov–Witten invariants of very ample hypersurfaces, Duke Math. J. 115 (2002) 171 MR1944571
38	H Geiges, Contact structures on 1-connected 5-manifolds, Mathematika 38 (1991) 303 MR1147828
39	F Gironella, Z Zhou, Exact orbifold fillings of contact manifolds, preprint (2021) arXiv:2108.12247
40	E Giroux, Une structure de contact, même tendue, est plus ou moins tordue, Ann. Sci. École Norm. Sup. 27 (1994) 697 MR1307678
41	M Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
42	J Harer, On handlebody structures for hypersurfaces in ℂ³ and ℂP³, Math. Ann. 238 (1978) 51 MR510306
43	H Hofer, K Wysocki, E Zehnder, Polyfold and Fredholm theory, 72, Springer ([2021] ©2021) MR4298268
44	M Hutchings, Rational SFT using only q variables, I,II,III,IV, blog post (2013)
45	E N Ionel, T H Parker, Relative Gromov–Witten invariants, Ann. of Math. 157 (2003) 45 MR1954264
46	S Ishikawa, Construction of general symplectic field theory, preprint (2018) arXiv:1807.09455
47	A M Keating, Dehn twists and free subgroups of symplectic mapping class groups, J. Topol. 7 (2014) 436 MR3217627
48	J Kock, I Vainsencher, An invitation to quantum cohomology : Kontsevich’s formula for rational plane curves, 249, Birkhäuser (2007) MR2262630
49	O van Koert, Simple computations in prequantization bundles, note (2014)
50	M Kwon, O van Koert, Brieskorn manifolds in contact topology, Bull. Lond. Math. Soc. 48 (2016) 173 MR3483060
51	J Latschev, C Wendl, Algebraic torsion in contact manifolds, Geom. Funct. Anal. 21 (2011) 1144 MR2846386
52	O Lazarev, Contact manifolds with flexible fillings, Geom. Funct. Anal. 30 (2020) 188 MR4081058
53	O Lazarev, Maximal contact and symplectic structures, J. Topol. 13 (2020) 1058 MR4100126
54	O Lazarev, Z Sylvan, Prime-localized Weinstein subdomains, Geom. Topol. 27 (2023) 699 MR4589563
55	A Libgober, Lectures on topology of complements and fundamental groups, from: "Singularity theory" (editors D Chéniot, N Dutertre, C Murolo, D Trotman, A Pichon), World Sci. (2007) 71 MR2342909
56	P Lisca, G Matić, Tight contact structures and Seiberg–Witten invariants, Invent. Math. 129 (1997) 509 MR1465333
57	S Lisi, J Van Horn-Morris, C Wendl, On symplectic fillings of spinal open book decompositions, I: Geometric constructions, preprint (2018) arXiv:1810.12017
58	P Massot, K Niederkrüger, C Wendl, Weak and strong fillability of higher dimensional contact manifolds, Invent. Math. 192 (2013) 287 MR3044125
59	M McLean, The growth rate of symplectic homology and affine varieties, Geom. Funct. Anal. 22 (2012) 369 MR2929069
60	M McLean, Symplectic invariance of uniruled affine varieties and log Kodaira dimension, Duke Math. J. 163 (2014) 1929 MR3229045
61	M McLean, Computing symplectic homology of affine varieties, talk slides (2016)
62	M McLean, Reeb orbits and the minimal discrepancy of an isolated singularity, Invent. Math. 204 (2016) 505 MR3489704
63	J Milnor, Morse theory, 51, Princeton Univ. Press (1963) MR163331
64	A Moreno, Algebraic torsion in higher-dimensional contact manifolds, PhD thesis, Humboldt-Universität zu Berlin (2018)
65	A Moreno, Pseudo-holomorphic dynamics in the restricted three-body problem, Math. Proc. Cambridge Philos. Soc. 174 (2023) 663 MR4574648
66	A Moreno, R Siefring, Holomorphic curves in the presence of holomorphic hypersurface foliations, preprint (2019) arXiv:1902.02700
67	A Moreno, Z Zhou, RSFT functors for strong cobordisms and applications, preprint (2023) arXiv:2308.00370
68	K L Nguyen, On the complement of a positive normal crossing divisor with no triple intersection in a projective variety, preprint (2015) arXiv:1512.08537
69	K Niederkrüger, C Wendl, Weak symplectic fillings and holomorphic curves, Ann. Sci. Éc. Norm. Supér. 44 (2011) 801 MR2931519
70	P Ozsváth, A Stipsicz, Z Szabó, Planar open books and Floer homology, Int. Math. Res. Not. 2005 (2005) 3385 MR2200085
71	J Pardon, An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves, Geom. Topol. 20 (2016) 779 MR3493097
72	J Pardon, Contact homology and virtual fundamental cycles, J. Amer. Math. Soc. 32 (2019) 825 MR3981989
73	A F Ritter, Floer theory for negative line bundles via Gromov–Witten invariants, Adv. Math. 262 (2014) 1035 MR3228449
74	P Seidel, A biased view of symplectic cohomology, from: "Current developments in mathematics, 2006" (editors B Mazur, T Mrowka, W Schmid, R Stanley, S T Yau), International (2008) 211 MR2459307
75	P Seidel, J P Solomon, Symplectic cohomology and q-intersection numbers, Geom. Funct. Anal. 22 (2012) 443 MR2929070
76	K Siegel, Higher symplectic capacities, preprint (2019) arXiv:1902.01490
77	J Stasheff, Differential graded Lie algebras, quasi-Hopf algebras and higher homotopy algebras, from: "Quantum groups" (editor P P Kulish), Lecture Notes in Math. 1510, Springer (1992) 120 MR1183483
78	M F Tehrani, M McLean, A Zinger, Normal crossings singularities for symplectic topology, Adv. Math. 339 (2018) 672 MR3866910
79	A Wand, Tightness is preserved by Legendrian surgery, Ann. of Math. 182 (2015) 723 MR3418529
80	C Wendl, Open book decompositions and stable Hamiltonian structures, Expo. Math. 28 (2010) 187 MR2671115
81	C Wendl, Strongly fillable contact manifolds and J-holomorphic foliations, Duke Math. J. 151 (2010) 337 MR2605865
82	C Wendl, A hierarchy of local symplectic filling obstructions for contact 3-manifolds, Duke Math. J. 162 (2013) 2197 MR3102479
83	C Wendl, Non-exact symplectic cobordisms between contact 3-manifolds, J. Differential Geom. 95 (2013) 121 MR3128981
84	C Wendl, Lectures on symplectic field theory, preprint (2016) arXiv:1612.01009
85	M L Yau, Vanishing of the contact homology of overtwisted contact 3-manifolds, Bull. Inst. Math. Acad. Sin. 1 (2006) 211 MR2230587
86	Z Zhou, Quotient theorems in polyfold theory and S¹-equivariant transversality, Proc. Lond. Math. Soc. 121 (2020) 1337 MR4133710
87	Z Zhou, (ℝℙ²ⁿ⁻¹,ξ_std) is not exactly fillable for n≠2^k, Geom. Topol. 25 (2021) 3013 MR4347310
88	Z Zhou, Symplectic fillings of asymptotically dynamically convex manifolds, I, J. Topol. 14 (2021) 112 MR4186135
89	Z Zhou, On the minimal symplectic area of Lagrangians, J. Symplectic Geom. 20 (2022) 1385 MR4583963
90	Z Zhou, Symplectic fillings of asymptotically dynamically convex manifolds, II : k-dilations, Adv. Math. 406 (2022) 108522 MR4438065
91	Z Zhou, On fillings of ∂(V × 𝔻), Math. Ann. 385 (2023) 1493 MR4566698