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Multisections of Lefschetz fibrations and topology of symplectic $4$–manifolds

R İnanç Baykur and Kenta Hayano

Geometry & Topology 20 (2016) 2335–2395
Bibliography
1 S Akbulut, R Kirby, Branched covers of surfaces in 4–manifolds, Math. Ann. 252 (1979/80) 111 MR593626
2 S Akbulut, B Ozbagci, Lefschetz fibrations on compact Stein surfaces, Geom. Topol. 5 (2001) 319 MR1825664
3 D Auroux, L Katzarkov, A degree doubling formula for braid monodromies and Lefschetz pencils, Pure Appl. Math. Q. 4 (2008) 237 MR2400878
4 S Bauer, Almost complex 4–manifolds with vanishing first Chern class, J. Differential Geom. 79 (2008) 25 MR2414748
5 R İ Baykur, Topology of broken Lefschetz fibrations and near-symplectic four-manifolds, Pacific J. Math. 240 (2009) 201 MR2485463
6 R I Baykur, Inequivalent Lefschetz fibrations and surgery equivalence of symplectic 4–manifolds, J. Symplectic Geom. 14 (2016) 671
7 R İ Baykur, Minimality and fiber sum decompositions of Lefschetz fibrations, Proc. Amer. Math. Soc. 144 (2016) 2275 MR3460185
8 R I Baykur, K Hayano, Hurwitz equivalence for Lefschetz fibrations and their multisections, to appear in Contemp. Math., "Proceedings of the 13th International Workshop on Real and Complex Singularities" (2015) arXiv:1504.03051
9 P Bellingeri, S Gervais, Surface framed braids, Geom. Dedicata 159 (2012) 51 MR2944520
10 S K Donaldson, Lefschetz pencils on symplectic manifolds, J. Differential Geom. 53 (1999) 205 MR1802722
11 S Donaldson, I Smith, Lefschetz pencils and the canonical class for symplectic four-manifolds, Topology 42 (2003) 743 MR1958528
12 J G Dorfmeister, Kodaira dimension of fiber sums along spheres, Geom. Dedicata 177 (2015) 1 MR3370019
13 H Endo, Meyer’s signature cocycle and hyperelliptic fibrations, Math. Ann. 316 (2000) 237 MR1741270
14 H Endo, Y Z Gurtas, Lantern relations and rational blowdowns, Proc. Amer. Math. Soc. 138 (2010) 1131 MR2566578
15 B Farb, D Margalit, A primer on mapping class groups, 49, Princeton Univ. Press (2012) MR2850125
16 S Finashin, Knotting of algebraic curves in P2, Topology 41 (2002) 47 MR1871240
17 R Fintushel, R J Stern, Rational blowdowns of smooth 4–manifolds, J. Differential Geom. 46 (1997) 181 MR1484044
18 R Fintushel, R J Stern, Surfaces in 4–manifolds, Math. Res. Lett. 4 (1997) 907 MR1492129
19 R Fintushel, R J Stern, Knots, links, and 4–manifolds, Invent. Math. 134 (1998) 363 MR1650308
20 R Fintushel, R J Stern, Families of simply connected 4–manifolds with the same Seiberg–Witten invariants, Topology 43 (2004) 1449 MR2081432
21 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
22 S Friedl, S Vidussi, On the topology of symplectic Calabi–Yau 4–manifolds, J. Topol. 6 (2013) 945 MR3145145
23 D Gay, T E Mark, Convex plumbings and Lefschetz fibrations, J. Symplectic Geom. 11 (2013) 363 MR3100798
24 R E Gompf, A new construction of symplectic manifolds, Ann. of Math. 142 (1995) 527 MR1356781
25 R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, 20, Amer. Math. Soc. (1999) MR1707327
26 I Hambleton, M Kreck, Smooth structures on algebraic surfaces with cyclic fundamental group, Invent. Math. 91 (1988) 53 MR918236
27 I Hambleton, M Kreck, Cancellation, elliptic surfaces and the topology of certain four-manifolds, J. Reine Angew. Math. 444 (1993) 79 MR1241794
28 A Kas, On the handlebody decomposition associated to a Lefschetz fibration, Pacific J. Math. 89 (1980) 89 MR596919
29 H J Kim, Modifying surfaces in 4–manifolds by twist spinning, Geom. Topol. 10 (2006) 27 MR2207789
30 H J Kim, D Ruberman, Topological triviality of smoothly knotted surfaces in 4–manifolds, Trans. Amer. Math. Soc. 360 (2008) 5869 MR2425695
31 M Korkmaz, Noncomplex smooth 4–manifolds with Lefschetz fibrations, Internat. Math. Res. Notices (2001) 115 MR1810689
32 M Korkmaz, B Ozbagci, On sections of elliptic fibrations, Michigan Math. J. 56 (2008) 77 MR2433657
33 T J Li, Smoothly embedded spheres in symplectic 4–manifolds, Proc. Amer. Math. Soc. 127 (1999) 609 MR1459135
34 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
35 T J Li, Quaternionic bundles and Betti numbers of symplectic 4–manifolds with Kodaira dimension zero, Int. Math. Res. Not. 2006 (2006) MR2264722
36 T J Li, Symplectic 4–manifolds with Kodaira dimension zero, J. Differential Geom. 74 (2006) 321 MR2259057
37 T J Li, A Liu, Symplectic structure on ruled surfaces and a generalized adjunction formula, Math. Res. Lett. 2 (1995) 453 MR1355707
38 A Loi, R Piergallini, Compact Stein surfaces with boundary as branched covers of B4, Invent. Math. 143 (2001) 325 MR1835390
39 G Massuyeau, A Oancea, D A Salamon, Lefschetz fibrations, intersection numbers, and representations of the framed braid group, Bull. Math. Soc. Sci. Math. Roumanie 56(104) (2013) 435 MR3157093
40 Y Matsumoto, Lefschetz fibrations of genus two—a topological approach, from: "Topology and Teichmüller spaces" (editors S Kojima, Y Matsumoto, K Saito, M Seppälä), World Sci. Publ. (1996) 123 MR1659687
41 D McDuff, M Symington, Associativity properties of the symplectic sum, Math. Res. Lett. 3 (1996) 591 MR1418574
42 W Meyer, Die Signatur von Flächenbündeln, Math. Ann. 201 (1973) 239 MR0331382
43 B Ozbagci, Signatures of Lefschetz fibrations, Pacific J. Math. 202 (2002) 99 MR1883972
44 J Park, K H Yun, Nonisomorphic Lefschetz fibrations on knot surgery 4–manifolds, Math. Ann. 345 (2009) 581 MR2534109
45 Y Sato, 2–spheres of square 1 and the geography of genus–2 Lefschetz fibrations, J. Math. Sci. Univ. Tokyo 15 (2008) 461 MR2546906
46 Y Sato, Canonical classes and the geography of nonminimal Lefschetz fibrations over S2, Pacific J. Math. 262 (2013) 191 MR3069059
47 A Scorpan, The wild world of 4–manifolds, Amer. Math. Soc. (2005) MR2136212
48 B Siebert, G Tian, On the holomorphicity of genus two Lefschetz fibrations, Ann. of Math. 161 (2005) 959 MR2153404
49 I Smith, Geometric monodromy and the hyperbolic disc, Q. J. Math. 52 (2001) 217 MR1838364
50 I Smith, Lefschetz pencils and divisors in moduli space, Geom. Topol. 5 (2001) 579 MR1833754
51 A I Stipsicz, Indecomposability of certain Lefschetz fibrations, Proc. Amer. Math. Soc. 129 (2001) 1499 MR1712877
52 N S Sunukjian, Surfaces in 4–manifolds : concordance, isotopy, and surgery, Int. Math. Res. Not. 2015 (2015) 7950 MR3404006
53 C H Taubes, The Seiberg–Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994) 809 MR1306023
54 C H Taubes, SW Gr : from the Seiberg–Witten equations to pseudo-holomorphic curves, J. Amer. Math. Soc. 9 (1996) 845 MR1362874
55 M Usher, Minimality and symplectic sums, Int. Math. Res. Not. 2006 (2006) MR2250015