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Surgery along star-shaped plumbings and exotic smooth structures on $4$–manifolds

Çağri Karakurt and Laura Starkston

Algebraic & Geometric Topology 16 (2016) 1585–1635
Bibliography
1 A Akhmedov, Small exotic 4–manifolds, Algebr. Geom. Topol. 8 (2008) 1781 MR2448872
2 A Akhmedov, R İ Baykur, B D Park, Constructing infinitely many smooth structures on small 4–manifolds, J. Topol. 1 (2008) 409 MR2399137
3 A Akhmedov, B D Park, Exotic smooth structures on small 4–manifolds, Invent. Math. 173 (2008) 209 MR2403396
4 A Akhmedov, B D Park, Exotic smooth structures on small 4–manifolds with odd signatures, Invent. Math. 181 (2010) 577 MR2660453
5 S Baldridge, P Kirk, A symplectic manifold homeomorphic but not diffeomorphic to ℂℙ2#3ℂℙ2, Geom. Topol. 12 (2008) 919 MR2403801
6 M Bhupal, B Özbaǧci, Symplectic fillings of lens spaces as Lefschetz fibrations (2013) arXiv:1307.6935
7 M Bhupal, A I Stipsicz, Weighted homogeneous singularities and rational homology disk smoothings, Amer. J. Math. 133 (2011) 1259 MR2843099
8 V Colin, P Ghiggini, K Honda, Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions, Proc. Natl. Acad. Sci. USA 108 (2011) 8100 MR2806645
9 S K Donaldson, Irrationality and the h–cobordism conjecture, J. Differential Geom. 26 (1987) 141 MR892034
10 H Endo, Y Z Gurtas, Lantern relations and rational blowdowns, Proc. Amer. Math. Soc. 138 (2010) 1131 MR2566578
11 H Endo, T E Mark, J Van Horn-Morris, Monodromy substitutions and rational blowdowns, J. Topol. 4 (2011) 227 MR2783383
12 J B Etnyre, B Özbaǧci, Invariants of contact structures from open books, Trans. Amer. Math. Soc. 360 (2008) 3133 MR2379791
13 R Fintushel, B D Park, R J Stern, Reverse engineering small 4–manifolds, Algebr. Geom. Topol. 7 (2007) 2103 MR2366188
14 R Fintushel, R J Stern, Rational blowdowns of smooth 4–manifolds, J. Differential Geom. 46 (1997) 181 MR1484044
15 R Fintushel, R J Stern, Knots, links, and 4–manifolds, Invent. Math. 134 (1998) 363 MR1650308
16 R Fintushel, R J Stern, Double node neighborhoods and families of simply connected 4–manifolds with b+ = 1, J. Amer. Math. Soc. 19 (2006) 171 MR2169045
17 R Fintushel, R J Stern, Six lectures on four 4–manifolds, from: "Low dimensional topology" (editors T S Mrowka, P S Ozsváth), IAS/Park City Math. Ser. 15, Amer. Math. Soc. (2009) 265 MR2503498
18 R Fintushel, R J Stern, Pinwheels and nullhomologous surgery on 4–manifolds with b+ = 1, Algebr. Geom. Topol. 11 (2011) 1649 MR2821436
19 M H Freedman, The topology of four-dimensional manifolds, J. Differential Geom. 17 (1982) 357 MR679066
20 R Friedman, J W Morgan, On the diffeomorphism types of certain algebraic surfaces. I, J. Differential Geom. 27 (1988) 297 MR925124
21 D Gay, T E Mark, Convex plumbings and Lefschetz fibrations, J. Symplectic Geom. 11 (2013) 363 MR3100798
22 D T Gay, A I Stipsicz, Symplectic rational blow-down along Seifert fibered 3–manifolds, Int. Math. Res. Not. 2007 (2007) 20 MR2376205
23 D T Gay, A I Stipsicz, Symplectic surgeries and normal surface singularities, Algebr. Geom. Topol. 9 (2009) 2203 MR2558309
24 R E Gompf, Handlebody construction of Stein surfaces, Ann. of Math. 148 (1998) 619 MR1668563
25 D Kotschick, On manifolds homeomorphic to CP2#8CP2, Invent. Math. 95 (1989) 591 MR979367
26 Ç Kutluhan, Y J Lee, C H Taubes, HF = HM I : Heegaard Floer homology and Seiberg–Witten Floer homology (2010) arXiv:1007.1979
27 T J Li, The Kodaira dimension of symplectic 4–manifolds, 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) 249 MR2249257
28 T J Li, A Liu, Symplectic structure on ruled surfaces and a generalized adjunction formula, Math. Res. Lett. 2 (1995) 453 MR1355707
29 D McDuff, D Salamon, Introduction to symplectic topology, , The Clarendon Press Oxford University Press (1995) MR1373431
30 M Michalogiorgaki, Rational blow-down along Wahl type plumbing trees of spheres, Algebr. Geom. Topol. 7 (2007) 1327 MR2350284
31 J W Morgan, The Seiberg–Witten equations and applications to the topology of smooth four-manifolds, 44, Princeton Univ. Press (1996) MR1367507
32 P Ozsváth, Z Szabó, The symplectic Thom conjecture, Ann. of Math. 151 (2000) 93 MR1745017
33 P Ozsváth, Z Szabó, Holomorphic triangle invariants and the topology of symplectic four-manifolds, Duke Math. J. 121 (2004) 1 MR2031164
34 H Park, A I Stipsicz, Smoothings of singularities and symplectic surgery (2012) arXiv:1211.6830v1
35 J Park, Seiberg–Witten invariants of generalised rational blow-downs, Bull. Austral. Math. Soc. 56 (1997) 363 MR1490654
36 J Park, Simply connected symplectic 4–manifolds with b2+ = 1 and c12 = 2, Invent. Math. 159 (2005) 657 MR2125736
37 J Park, A I Stipsicz, Z Szabó, Exotic smooth structures on ℂℙ2#5ℂℙ2, Math. Res. Lett. 12 (2005) 701 MR2189231
38 U Persson, Configurations of Kodaira fibers on rational elliptic surfaces, Math. Z. 205 (1990) 1 MR1069483
39 L P Roberts, Rational blow-downs in Heegaard–Floer homology, Commun. Contemp. Math. 10 (2008) 491 MR2444846
40 L Starkston, Comparing star surgery to rational blow-down (2014) arXiv:1407.3293
41 L Starkston, Symplectic fillings of Seifert fibered spaces, Trans. Amer. Math. Soc. 367 (2015) 5971 MR3347194
42 A I Stipsicz, Z Szabó, An exotic smooth structure on ℂℙ2#6ℂℙ2, Geom. Topol. 9 (2005) 813 MR2140993
43 A I Stipsicz, Z Szabó, J Wahl, Rational blowdowns and smoothings of surface singularities, J. Topol. 1 (2008) 477 MR2399141
44 M Symington, Symplectic rational blowdowns, J. Differential Geom. 50 (1998) 505 MR1690738
45 M Symington, Generalized symplectic rational blowdowns, Algebr. Geom. Topol. 1 (2001) 503 MR1852770
46 Z Szabó, Exotic 4–manifolds with b2+ = 1, Math. Res. Lett. 3 (1996) 731 MR1426531
47 C Wendl, Strongly fillable contact manifolds and J–holomorphic foliations, Duke Math. J. 151 (2010) 337 MR2605865