Algebraic & Geometric Topology Volume 10, issue 2 (2010)

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On nonseparating contact hypersurfaces in symplectic $4$–manifolds

Peter Albers, Barney Bramham and Chris Wendl

Algebraic & Geometric Topology 10 (2010) 697–737

DOI: 10.2140/agt.2010.10.697

Bibliography

1	C Abbas, Holomorphic open book decompositions arXiv:0907.3512
2	M Bhupal, K Ono, Symplectic fillings of links of quotient surface singularities arXiv:0808.3794
3	F Bourgeois, Y Eliashberg, H Hofer, K Wysocki, E Zehnder, Compactness results in symplectic field theory, Geom. Topol. 7 (2003) 799 MR2026549
4	Y Eliashberg, Filling by holomorphic discs and its applications, from: "Geometry of low-dimensional manifolds, 2 (Durham, 1989)" (editors S K Donaldson, C B Thomas), London Math. Soc. Lecture Note Ser. 151, Cambridge Univ. Press (1990) 45 MR1171908
5	Y Eliashberg, A few remarks about symplectic filling, Geom. Topol. 8 (2004) 277 MR2023279
6	J B Etnyre, Planar open book decompositions and contact structures, Int. Math. Res. Not. (2004) 4255 MR2126827
7	J B Etnyre, private communication (2008)
8	J B Etnyre, K Honda, On symplectic cobordisms, Math. Ann. 323 (2002) 31 MR1906906
9	J B Etnyre, J Van Horn-Morris, Fibered transverse knots and the Bennequin bound arXiv:0803.0758
10	D T Gay, Four-dimensional symplectic cobordisms containing three-handles, Geom. Topol. 10 (2006) 1749 MR2284049
11	H Geiges, Examples of symplectic $4$–manifolds with disconnected boundary of contact type, Bull. London Math. Soc. 27 (1995) 278 MR1328705
12	H Geiges, Constructions of contact manifolds, Math. Proc. Cambridge Philos. Soc. 121 (1997) 455 MR1434654
13	H Geiges, An introduction to contact topology, Cambridge Studies in Advanced Math. 109, Cambridge Univ. Press (2008) MR2397738
14	E Giroux, Links and contact structures, Lecture notes, Georgia Topology Conference (2001)
15	M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
16	M Gromov, Partial differential relations, Ergebnisse der Math. und ihrer Grenzgebiete (3) 9, Springer (1986) MR864505
17	H Hofer, Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993) 515 MR1244912
18	H Hofer, V Lizan, J C Sikorav, On genericity for holomorphic curves in four-dimensional almost-complex manifolds, J. Geom. Anal. 7 (1997) 149 MR1630789
19	H Hofer, K Wysocki, E Zehnder, Properties of pseudo-holomorphic curves in symplectisations. II. Embedding controls and algebraic invariants, Geom. Funct. Anal. 5 (1995) 270 MR1334869
20	H Hofer, K Wysocki, E Zehnder, Properties of pseudoholomorphic curves in symplectisation. IV. Asymptotics with degeneracies, from: "Contact and symplectic geometry (Cambridge, 1994)" (editor C B Thomas), Publ. Newton Inst. 8, Cambridge Univ. Press (1996) 78 MR1432460
21	H Hofer, K Wysocki, E Zehnder, Properties of pseudoholomorphic curves in symplectisations. I. Asymptotics, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996) 337 MR1395676
22	H Hofer, K Wysocki, E Zehnder, Properties of pseudoholomorphic curves in symplectizations. III. Fredholm theory, from: "Topics in nonlinear analysis" (editors J Escher, G Simonett), Progr. Nonlinear Differential Equations Appl. 35, Birkhäuser (1999) 381 MR1725579
23	C Hummel, Gromov's compactness theorem for pseudo-holomorphic curves, Progress in Math. 151, Birkhäuser Verlag (1997) MR1451624
24	Y Kanda, The classification of tight contact structures on the $3$–torus, Comm. Anal. Geom. 5 (1997) 413 MR1487723
25	R Lutz, Structures de contact sur les fibrés principaux en cercles de dimension trois, Ann. Inst. Fourier (Grenoble) 27 (1977) 1 MR0478180
26	D McDuff, The structure of rational and ruled symplectic $4$–manifolds, J. Amer. Math. Soc. 3 (1990) 679 MR1049697
27	D McDuff, Symplectic manifolds with contact type boundaries, Invent. Math. 103 (1991) 651 MR1091622
28	D McDuff, D Salamon, $J$–holomorphic curves and symplectic topology, Amer. Math. Soc. Coll. Publ. 52, Amer. Math. Soc. (2004) MR2045629
29	E Mora, Pseudoholomorphic cylinders in symplectisations, PhD thesis, New York University (2003)
30	H Ohta, K Ono, Simple singularities and symplectic fillings, J. Differential Geom. 69 (2005) 1 MR2169581
31	R Siefring, Intersection theory of punctured pseudoholomorphic curves arXiv:0907.0470
32	R Siefring, C Wendl, Pseudoholomorphic curves, intersections and Morse–Bott asymptotics, in preparation
33	J Y Welschinger, Effective classes and Lagrangian tori in symplectic four-manifolds, J. Symplectic Geom. 5 (2007) 9 MR2371182
34	C Wendl, Automatic transversality and orbifolds of punctured holomorphic curves in dimension four, to appear in Comment. Math. Helv. arXiv:0802.3842
35	C Wendl, Compactness for embedded pseudoholomorphic curves in $3$–manifolds, to appear in J. Eur. Math. Soc. (JEMS) arXiv:math/0703509
36	C Wendl, Contact fiber sums, monodromy maps and symplectic fillings, in preparation
37	C Wendl, Holomorphic curves in blown up open books arXiv:1001.4109
38	C Wendl, Open book decompositions and stable Hamiltonian structures, to appear in Expos. Math. arXiv:0808.3220
39	C Wendl, Punctured holomorphic curves with boundary in $3$–manifolds: Fredholm theory and embededdness, in preparation
40	C Wendl, Strongly fillable contact manifolds and $J$–holomorphic foliations, to appear in Duke Math. J. arXiv:0806.3193
41	C Wendl, Finite energy foliations and surgery on transverse links, PhD thesis, New York University (2005)
42	K Zehmisch, The Eliashberg–Gromov tightness theorem, Diplom Thesis, Universität Leipzig (2003)