Download this article
 Download this article For screen
For printing
Recent Issues

Volume 29, 1 issue

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Homological invariants of codimension $2$ contact submanifolds

Laurent Côté and François-Simon Fauteux-Chapleau

Geometry & Topology 28 (2024) 1–125
Bibliography
1 R Abraham, Bumpy metrics, from: "Global analysis" (editors S s Chern, S Smale), Proc. Sympos. Pure Math. XIV, Amer. Math. Soc. (1970) 1 MR0271994
2 P Albers, B Bramham, C Wendl, On nonseparating contact hypersurfaces in symplectic 4–manifolds, Algebr. Geom. Topol. 10 (2010) 697 MR2606798
3 M R R Alves, A Pirnapasov, Reeb orbits that force topological entropy, Ergodic Theory Dynam. Systems 42 (2022) 3025 MR4476096
4 E Bao, K Honda, Definition of cylindrical contact homology in dimension three, J. Topol. 11 (2018) 1002 MR3989436
5 M S Borman, Y Eliashberg, E Murphy, Existence and classification of overtwisted contact structures in all dimensions, Acta Math. 215 (2015) 281 MR3455235
6 F Bourgeois, A Morse–Bott approach to contact homology, PhD thesis, Stanford University (2002)
7 F Bourgeois, T Ekholm, Y Eliashberg, Effect of Legendrian surgery, Geom. Topol. 16 (2012) 301 MR2916289
8 F Bourgeois, O van Koert, Contact homology of left-handed stabilizations and plumbing of open books, Commun. Contemp. Math. 12 (2010) 223 MR2646902
9 J Bowden, Two-dimensional foliations on four-manifolds, PhD thesis, Ludwig Maximilian University of Munich (2010)
10 R Casals, J B Etnyre, Non-simplicity of isocontact embeddings in all higher dimensions, Geom. Funct. Anal. 30 (2020) 1 MR4081055
11 R Casals, E Murphy, Legendrian fronts for affine varieties, Duke Math. J. 168 (2019) 225 MR3909897
12 R Casals, E Murphy, F Presas, Geometric criteria for overtwistedness, J. Amer. Math. Soc. 32 (2019) 563 MR3904160
13 R Casals, D M Pancholi, F Presas, The Legendrian Whitney trick, Geom. Topol. 25 (2021) 3229 MR4347315
14 B Chantraine, Lagrangian concordance of Legendrian knots, Algebr. Geom. Topol. 10 (2010) 63 MR2580429
15 B Chantraine, G Dimitroglou Rizell, P Ghiggini, R Golovko, Floer theory for Lagrangian cobordisms, J. Differential Geom. 114 (2020) 393 MR4072203
16 K Cieliebak, Y Eliashberg, From Stein to Weinstein and back : symplectic geometry of affine complex manifolds, 59, Amer. Math. Soc. (2012) MR3012475
17 A Connes, Noncommutative differential geometry, Inst. Hautes Études Sci. Publ. Math. 62 (1985) 257 MR823176
18 M Dörner, H Geiges, K Zehmisch, Open books and the Weinstein conjecture, Q. J. Math. 65 (2014) 869 MR3261972
19 T Ekholm, Rational SFT, linearized Legendrian contact homology, and Lagrangian Floer cohomology, from: "Perspectives in analysis, geometry, and topology" (editors I Itenberg, B Jöricke, M Passare), Progr. Math. 296, Springer (2012) 109 MR2884034
20 T Ekholm, Holomorphic curves for Legendrian surgery, preprint (2019) arXiv:1906.07228
21 T Ekholm, J Etnyre, L Ng, M Sullivan, Filtrations on the knot contact homology of transverse knots, Math. Ann. 355 (2013) 1561 MR3037024
22 T Ekholm, J B Etnyre, L Ng, M G Sullivan, Knot contact homology, Geom. Topol. 17 (2013) 975 MR3070519
23 T Ekholm, K Honda, T Kálmán, Legendrian knots and exact Lagrangian cobordisms, J. Eur. Math. Soc. 18 (2016) 2627 MR3562353
24 Y Eliashberg, A Givental, H Hofer, Introduction to symplectic field theory, from: "Visions in mathematics: GAFA 2000 special volume, II" (editors N Alon, J Bourgain, A Connes, M Gromov, V Milman), Birkhäuser (2000) 560 MR1826267
25 Y Eliashberg, N Mishachev, Introduction to the h–principle, 48, Amer. Math. Soc. (2002) MR1909245
26 Y Eliashberg, E Murphy, Lagrangian caps, Geom. Funct. Anal. 23 (2013) 1483 MR3102911
27 J B Etnyre, L L Ng, Legendrian contact homology in 3, from: "Surveys in differential geometry 2020 : surveys in 3–manifold topology and geometry" (editors I Agol, D Gabai), Surv. Differ. Geom. 25, International ([2022] ©2022) 103 MR4479751
28 J B Etnyre, D S Vela-Vick, Torsion and open book decompositions, Int. Math. Res. Not. 2010 (2010) 4385 MR2737776
29 H Geiges, An introduction to contact topology, 109, Cambridge Univ. Press (2008) MR2397738
30 M Gerstenhaber, C W Wilkerson, On the deformation of rings and algebras, V : Deformation of differential graded algebras, from: "Higher homotopy structures in topology and mathematical physics" (editor J McCleary), Contemp. Math. 227, Amer. Math. Soc. (1999) 89 MR1665463
31 E Giroux, Géométrie de contact : de la dimension trois vers les dimensions supérieures, from: "Proceedings of the International Congress of Mathematicians, II" (editor T Li), Higher Ed. (2002) 405 MR1957051
32 P Griffiths, J Morgan, Rational homotopy theory and differential forms, 16, Springer (2013) MR3136262
33 J Gutt, The Conley–Zehnder index for a path of symplectic matrices, preprint (2012) arXiv:1201.3728v2
34 V Hinich, Homological algebra of homotopy algebras, Comm. Algebra 25 (1997) 3291 MR1465117
35 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
36 H Hofer, K Wysocki, E Zehnder, A general Fredholm theory, I : A splicing-based differential geometry, J. Eur. Math. Soc. 9 (2007) 841 MR2341834
37 H Hofer, K Wysocki, E Zehnder, A general Fredholm theory, II : Implicit function theorems, Geom. Funct. Anal. 19 (2009) 206 MR2507223
38 H Hofer, K Wysocki, E Zehnder, A general Fredholm theory, III : Fredholm functors and polyfolds, Geom. Topol. 13 (2009) 2279 MR2515707
39 K Honda, Y Huang, Convex hypersurface theory in contact topology, preprint (2019) arXiv:1907.06025
40 U Hryniewicz, A Momin, P A S Salomão, A Poincaré–Birkhoff theorem for tight Reeb flows on S3, Invent. Math. 199 (2015) 333 MR3302117
41 M Hutchings, Mean action and the Calabi invariant, J. Mod. Dyn. 10 (2016) 511 MR3570996
42 M Hutchings, J Nelson, Cylindrical contact homology for dynamically convex contact forms in three dimensions, J. Symplectic Geom. 14 (2016) 983 MR3601881
43 P J Kahn, Obstructions to extending almost X–structures, Illinois J. Math. 13 (1969) 336 MR0258037
44 W Klingenberg, Lectures on closed geodesics, 230, Springer (1978) MR0478069
45 M Klukas, Open books and exact symplectic cobordisms, Internat. J. Math. 29 (2018) 1850026, 19 MR3797193
46 O van Koert, Lecture notes on stabilization of contact open books, Münster J. Math. 10 (2017) 425 MR3725503
47 A Lazarev, M Markl, Disconnected rational homotopy theory, Adv. Math. 283 (2015) 303 MR3383805
48 O Lazarev, Maximal contact and symplectic structures, J. Topol. 13 (2020) 1058 MR4100126
49 W Li, Lagrangian cobordism functor in microlocal sheaf theory, I, J. Topol. 16 (2023) 1113 MR4638002
50 J L Loday, Cyclic homology, 301, Springer (1998) MR1600246
51 J L Loday, B Vallette, Algebraic operads, 346, Springer (2012) MR2954392
52 D McDuff, D Salamon, Introduction to symplectic topology, Oxford Univ. Press (2017) MR3674984
53 A Momin, Contact homology of orbit complements and implied existence, J. Mod. Dyn. 5 (2011) 409
54 A Moreno, R Siefring, Holomorphic curves in the presence of holomorphic hypersurface foliations, preprint (2019) arXiv:1902.02700v1
55 E Murphy, Loose Legendrian embeddings in high dimensional contact manifolds, preprint (2019) arXiv:1201.2245v5
56 L Ng, Framed knot contact homology, Duke Math. J. 141 (2008) 365 MR2376818
57 L Ng, A topological introduction to knot contact homology, from: "Contact and symplectic topology" (editors F Bourgeois, V Colin, A Stipsicz), Bolyai Soc. Math. Stud. 26, János Bolyai Math. Soc. (2014) 485 MR3220948
58 L Ng, D Rutherford, V Shende, S Sivek, E Zaslow, Augmentations are sheaves, Geom. Topol. 24 (2020) 2149 MR4194293
59 D M Pancholi, S Pandit, Iso-contact embeddings of manifolds in codimension 2, J. Symplectic Geom. 20 (2022) 471 MR4537128
60 J Pardon, An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves, Geom. Topol. 20 (2016) 779 MR3493097
61 J Pardon, Contact homology and virtual fundamental cycles, J. Amer. Math. Soc. 32 (2019) 825 MR3981989
62 A Ranicki, High-dimensional knot theory : algebraic surgery in codimension 2, Springer (1998) MR1713074
63 J M Sabloff, L Traynor, Obstructions to Lagrangian cobordisms between Legendrians via generating families, Algebr. Geom. Topol. 13 (2013) 2733 MR3116302
64 R Siefring, Intersection theory of punctured pseudoholomorphic curves, Geom. Topol. 15 (2011) 2351 MR2862160
65 I Ustilovsky, Contact homology and contact structures on S4m+1, PhD thesis, Stanford University (1999)
66 B Vallette, Homotopy theory of homotopy algebras, Ann. Inst. Fourier (Grenoble) 70 (2020) 683 MR4105949
67 C Wendl, A hierarchy of local symplectic filling obstructions for contact 3–manifolds, Duke Math. J. 162 (2013) 2197 MR3102479
68 C Wendl, Lectures on symplectic field theory, preprint (2016) arXiv:1612.01009
69 C Wendl, Lectures on contact 3–manifolds, holomorphic curves and intersection theory, 220, Cambridge Univ. Press (2020) MR4211775
70 Z Zhou, Infinite not contact isotopic embeddings in (S2n1std) for n 4, Bull. Lond. Math. Soc. 55 (2023) 149 MR4561241