#### Volume 19 (2015)

 Download this article For screen For printing
 Recent Volumes Volume 1, 1998 Volume 2, 1999 Volume 3, 2000 Volume 4, 2002 Volume 5, 2002 Volume 6, 2003 Volume 7, 2004 Volume 8, 2006 Volume 9, 2006 Volume 10, 2007 Volume 11, 2007 Volume 12, 2007 Volume 13, 2008 Volume 14, 2008 Volume 15, 2008 Volume 16, 2009 Volume 17, 2011 Volume 18, 2012 Volume 19, 2015
 The Series About this Series Ethics Statement Purchase Printed Copies Author Index ISSN (electronic): 1464-8997 ISSN (print): 1464-8989 MSP Books and Monographs Other MSP Publications
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