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On the topology of fillings of contact $3$–manifolds

Burak Ozbagci

Geometry & Topology Monographs 19 (2015) 73–123
Bibliography
1 S Akbulut, R Matveyev, Exotic structures and adjunction inequality, Turkish J. Math. 21 (1997) 47 MR1456158
2 S Akbulut, B Ozbagci, Lefschetz fibrations on compact Stein surfaces, Geom. Topol. 5 (2001) 319 MR1825664
3 S Akbulut, B Ozbagci, Lefschetz fibrations on compact Stein surfaces : erratum, Geom. Topol. 5 (2001) 939
4 S Akbulut, B Ozbagci, On the topology of compact Stein surfaces, Int. Math. Res. Not. 2002 (2002) 769 MR1891172
5 S Akbulut, K Yasui, Infinitely many small exotic Stein fillings, J. Symplectic Geom. 12 (2014) 673 MR3333026
6 A Akhmedov, J B Etnyre, T E Mark, I Smith, A note on Stein fillings of contact manifolds, Math. Res. Lett. 15 (2008) 1127 MR2470389
7 A Akhmedov, B Ozbagci, Exotic Stein fillings with arbitrary fundamental group, preprint (2013) arXiv:1212.1743
8 K L Baker, J B Etnyre, J Van Horn-Morris, Cabling, contact structures and mapping class monoids, J. Differential Geom. 90 (2012) 1 MR2891477
9 R I Baykur, J V Horn-Morris, Topological complexity of symplectic 4–manifolds and Stein fillings, preprint (2012) arXiv:1212.1699
10 R I Baykur, J V Horn-Morris, S Lisi, C Wendl, Families of contact 3–manifolds with arbitrarily large Stein fillings, J. Diff. Geom. 101 (2015) 423
11 R I Baykur, M Korkmaz, N Monden, Sections of surface bundles and Lefschetz fibrations, Trans. Amer. Math. Soc. 365 (2013) 5999 MR3091273
12 M Bhupal, K Ono, Symplectic fillings of links of quotient surface singularities, Nagoya Math. J. 207 (2012) 1 MR2957141
13 M Bhupal, B Ozbagci, Symplectic fillings of lens spaces as Lefschetz fibrations, preprint (2013) arXiv:1307.6935
14 M Bhupal, B Ozbagci, Canonical contact structures on some singularity links, Bull. Lond. Math. Soc. 46 (2014) 576 MR3210714
15 M Bhupal, A I Stipsicz, Smoothings of singularities and symplectic topology, from: "Deformations of surface singularities" (editors A Némethi, Á Szilárd), Bolyai Soc. Math. Stud. 23, János Bolyai Math. Soc. (2013) 57 MR3203575
16 F A Bogomolov, B de Oliveira, Stein small deformations of strictly pseudoconvex surfaces, from: "Birational algebraic geometry" (editors Y Kawamata, V V Shokurov), Contemp. Math. 207, Amer. Math. Soc. (1997) 25 MR1462922
17 C Caubel, A Némethi, P Popescu-Pampu, Milnor open books and Milnor fillable contact 3-manifolds, Topology 45 (2006) 673 MR2218761
18 K Cieliebak, Y Eliashberg, From Stein to Weinstein and back : Symplectic geometry of affine complex manifolds, 59, Amer. Math. Soc. (2012) MR3012475
19 E Dalyan, M Korkmaz, M Pamuk, Arbitrarily long factorizations in mapping class groups, Int. Math. Res. Not. 2015 (2015) 9400
20 F Ding, H Geiges, Symplectic fillability of tight contact structures on torus bundles, Algebr. Geom. Topol. 1 (2001) 153 MR1823497
21 S K Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983) 279 MR710056
22 Y Eliashberg, Filling by holomorphic discs and its applications, from: "Geometry of low-dimensional manifolds, 2" (editors S K Donaldson, C B Thomas), London Math. Soc. Lecture Note Ser. 151, Cambridge Univ. Press (1990) 45 MR1171908
23 Y Eliashberg, Topological characterization of Stein manifolds of dimension > 2, Internat. J. Math. 1 (1990) 29 MR1044658
24 Y Eliashberg, On symplectic manifolds with some contact properties, J. Differential Geom. 33 (1991) 233 MR1085141
25 Y Eliashberg, Unique holomorphically fillable contact structure on the 3–torus, Internat. Math. Res. Notices (1996) 77 MR1383953
26 Y Eliashberg, A few remarks about symplectic filling, Geom. Topol. 8 (2004) 277 MR2023279
27 Y Eliashberg, M Gromov, Convex symplectic manifolds, from: "Several complex variables and complex geometry, Part 2" (editors E Bedford, J P D’Angelo, R E Greene, S G Krantz), Proc. Sympos. Pure Math. 52, Amer. Math. Soc. (1991) 135 MR1128541
28 H Endo, Y Z Gurtas, Lantern relations and rational blowdowns, Proc. Amer. Math. Soc. 138 (2010) 1131 MR2566578
29 H Endo, T E Mark, J Van Horn-Morris, Monodromy substitutions and rational blowdowns, J. Topol. 4 (2011) 227 MR2783383
30 T Etgü, B Ozbagci, Explicit horizontal open books on some plumbings, Internat. J. Math. 17 (2006) 1013 MR2274008
31 J B Etnyre, Symplectic convexity in low-dimensional topology, Topology Appl. 88 (1998) 3 MR1634561
32 J B Etnyre, On symplectic fillings, Algebr. Geom. Topol. 4 (2004) 73 MR2023278
33 J B Etnyre, Planar open book decompositions and contact structures, Int. Math. Res. Not. 2004 (2004) 4255 MR2126827
34 J B Etnyre, Lectures on open book decompositions and contact structures, from: "Floer homology, gauge theory, and low-dimensional topology" (editors D A Ellwood, P S Ozsváth, A I Stipsicz, Z Szabó), Clay Math. Proc. 5, Amer. Math. Soc. (2006) 103 MR2249250
35 J B Etnyre, K Honda, Tight contact structures with no symplectic fillings, Invent. Math. 148 (2002) 609 MR1908061
36 R Fintushel, R J Stern, Rational blowdowns of smooth 4–manifolds, J. Differential Geom. 46 (1997) 181 MR1484044
37 R Fintushel, R J Stern, Knots, links, and 4–manifolds, Invent. Math. 134 (1998) 363 MR1650308
38 D T Gay, Explicit concave fillings of contact three-manifolds, Math. Proc. Cambridge Philos. Soc. 133 (2002) 431 MR1919715
39 H Geiges, An introduction to contact topology, 109, Cambridge Univ. Press (2008) MR2397738
40 H Geiges, K Zehmisch, How to recognize a 4–ball when you see one, Münster J. Math. 6 (2013) 525 MR3148221
41 P Ghiggini, Strongly fillable contact 3–manifolds without Stein fillings, Geom. Topol. 9 (2005) 1677 MR2175155
42 E Giroux, Une structure de contact, même tendue, est plus ou moins tordue, Ann. Sci. École Norm. Sup. 27 (1994) 697 MR1307678
43 E Giroux, Géométrie de contact : de la dimension trois vers les dimensions supérieures, from: "Proceedings of the International Congress of Mathematicians, Vol. II" (editor T Li), Higher Ed. Press (2002) 405 MR1957051
44 R E Gompf, Handlebody construction of Stein surfaces, Ann. of Math. 148 (1998) 619 MR1668563
45 R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
46 H Grauert, On Levi’s problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958) 460 MR0098847
47 M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
48 K Honda, On the classification of tight contact structures, I, Geom. Topol. 4 (2000) 309 MR1786111
49 K Honda, On the classification of tight contact structures, II, J. Differential Geom. 55 (2000) 83 MR1849027
50 A Kaloti, Stein fillings of planar open books, preprint (2015) arXiv:1311.0208
51 A Kaloti, Y Li, Stein fillings of contact 3–manifolds obtained as Legendrian surgeries, preprint (2015) arXiv:1307.4726
52 M Korkmaz, Noncomplex smooth 4–manifolds with Lefschetz fibrations, Internat. Math. Res. Notices (2001) 115 MR1810689
53 M Korkmaz, B Ozbagci, On sections of elliptic fibrations, Michigan Math. J. 56 (2008) 77 MR2433657
54 Y Lekili, B Ozbagci, Milnor fillable contact structures are universally tight, Math. Res. Lett. 17 (2010) 1055 MR2729630
55 P Lisca, Symplectic fillings and positive scalar curvature, Geom. Topol. 2 (1998) 103 MR1633282
56 P Lisca, On symplectic fillings of 3–manifolds, from: "Proceedings of 6th Gökova Geometry–Topology Conference", Turkish J. Math. 23 (1999) 151 MR1701644
57 P Lisca, On symplectic fillings of lens spaces, Trans. Amer. Math. Soc. 360 (2008) 765 MR2346471
58 P Lisca, G Matić, Tight contact structures and Seiberg–Witten invariants, Invent. Math. 129 (1997) 509 MR1465333
59 P Lisca, G Matić, Stein 4–manifolds with boundary and contact structures, Topology Appl. 88 (1998) 55 MR1634563
60 P Lisca, A I Stipsicz, Ozsváth–Szabó invariants and tight contact three-manifolds, I, Geom. Topol. 8 (2004) 925 MR2087073
61 P Lisca, A I Stipsicz, Seifert fibered contact three-manifolds via surgery, Algebr. Geom. Topol. 4 (2004) 199 MR2059189
62 A Loi, R Piergallini, Compact Stein surfaces with boundary as branched covers of B4, Invent. Math. 143 (2001) 325 MR1835390
63 P Massot, K Niederkrüger, C Wendl, Weak and strong fillability of higher-dimensional contact manifolds, Invent. Math. 192 (2013) 287 MR3044125
64 D McDuff, The structure of rational and ruled symplectic 4–manifolds, J. Amer. Math. Soc. 3 (1990) 679 MR1049697
65 D McDuff, D Salamon, Introduction to symplectic topology, Oxford University Press (1998) MR1698616
66 A Némethi, Five lectures on normal surface singularities, from: "Low dimensional topology" (editors K Böröczky Jr., W Neumann, A Stipsicz), Bolyai Soc. Math. Stud. 8, János Bolyai Math. Soc., Budapest (1999) 269 MR1747271
67 A Némethi, Some meeting points of singularity theory and low dimensional topology, from: "Deformations of surface singularities" (editors A Némethi, Á Szilárd), Bolyai Soc. Math. Stud. 23, János Bolyai Math. Soc. (2013) 109 MR3203577
68 A Némethi, P Popescu-Pampu, On the Milnor fibres of cyclic quotient singularities, Proc. Lond. Math. Soc. 101 (2010) 554 MR2679701
69 K Niederkrüger, C Wendl, Weak symplectic fillings and holomorphic curves, Ann. Sci. Éc. Norm. Supér. 44 (2011) 801 MR2931519
70 H Ohta, K Ono, Simple singularities and topology of symplectically filling 4–manifold, Comment. Math. Helv. 74 (1999) 575 MR1730658
71 H Ohta, K Ono, Symplectic fillings of the link of simple elliptic singularities, J. Reine Angew. Math. 565 (2003) 183 MR2024651
72 H Ohta, K Ono, Simple singularities and symplectic fillings, J. Differential Geom. 69 (2005) 1 MR2169581
73 B Ozbagci, A I Stipsicz, Contact 3–manifolds with infinitely many Stein fillings, Proc. Amer. Math. Soc. 132 (2004) 1549 MR2053364
74 B Ozbagci, A I Stipsicz, Surgery on contact 3–manifolds and Stein surfaces, 13, Springer (2004) 281 MR2114165
75 O Plamenevskaya, Contact structures with distinct Heegaard Floer invariants, Math. Res. Lett. 11 (2004) 547 MR2092907
76 O Plamenevskaya, On Legendrian surgeries between lens spaces, J. Symplectic Geom. 10 (2012) 165 MR2926993
77 O Plamenevskaya, J Van Horn-Morris, Planar open books, monodromy factorizations and symplectic fillings, Geom. Topol. 14 (2010) 2077 MR2740642
78 S Schönenberger, Determining symplectic fillings from planar open books, J. Symplectic Geom. 5 (2007) 19 MR2371183
79 A Cannas da Silva, Lectures on symplectic geometry, 1764, Springer (2001) MR1853077
80 I Smith, Lefschetz pencils and divisors in moduli space, Geom. Topol. 5 (2001) 579 MR1833754
81 L Starkston, Symplectic fillings of Seifert fibered spaces, Trans. Amer. Math. Soc. 367 (2015) 5971 MR3347194
82 A I Stipsicz, Gauge theory and Stein fillings of certain 3–manifolds, Turkish J. Math. 26 (2002) 115 MR1892805
83 A I Stipsicz, On the geography of Stein fillings of certain 3–manifolds, Michigan Math. J. 51 (2003) 327 MR1992949
84 S Tanaka, On sections of hyperelliptic Lefschetz fibrations, Algebr. Geom. Topol. 12 (2012) 2259 MR3020206
85 C H Taubes, The Seiberg–Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994) 809 MR1306023
86 W P Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976) 467 MR0402764
87 W P Thurston, H E Winkelnkemper, On the existence of contact forms, Proc. Amer. Math. Soc. 52 (1975) 345 MR0375366
88 I Torisu, Convex contact structures and fibered links in 3–manifolds, Internat. Math. Res. Notices (2000) 441 MR1756943
89 J Van Horn-Morris, Constructions of open book decompositions, PhD thesis, Univ. Texas, Austin (2007) MR2710779
90 A Wand, Factorizations of diffeomorphisms of compact surfaces with boundary, Geom. Topol. 19 (2015) 2407
91 C Wendl, Strongly fillable contact manifolds and J–holomorphic foliations, Duke Math. J. 151 (2010) 337 MR2605865
92 C Wendl, Contact 3–manifolds, holomorphic curves and intersection theory (2013)
93 E Witten, Monopoles and four-manifolds, Math. Res. Lett. 1 (1994) 769 MR1306021