Stability and existence of surfaces in symplectic 4-manifolds with b⁺=1

References

[1] A. Akhmedov and J.-Y. Park, Lantern substitution and new symplectic 4-manifolds with b2+=3, preprint (2012), http://arxiv.org/abs/1207.0684. Search in Google Scholar

[2] T. Bauer et al., Recent developments and open problems in linear series, Contributions to algebraic geometry, EMS Ser. Congr. Rep., European Mathematical Society, Zürich (2012), 93–140. 10.4171/114-1/4Search in Google Scholar

[3] T. Bauer et al., Negative curves on algebraic surfaces, Duke Math. J. 162 (2013), no. 10, 1877–1894. 10.1215/00127094-2335368Search in Google Scholar

[4] P. Biran, A stability property of symplectic packing, Invent. Math. 136 (1999), no. 1, 123–155. 10.1007/s002220050306Search in Google Scholar

[5] P. Biran, Lagrangian barriers and symplectic embeddings, Geom. Funct. Anal. 11 (2001), no. 3, 407–464. 10.1007/PL00001678Search in Google Scholar

[6] M. S. Borman, T.-J. Li and W. Wu, Spherical Lagrangians via ball packings and symplectic cutting, preprint (2012), http://arxiv.org/abs/1211.5952. 10.1007/s00029-013-0120-zSearch in Google Scholar

[7] J. G. Dorfmeister and T.-J. Li, The relative symplectic cone and T2-fibrations, J. Symplectic Geom. 8 (2010), no. 1, 1–35. 10.4310/JSG.2010.v8.n1.a1Search in Google Scholar

[8] T. Etgü and B. D. Park, Non-isotopic symplectic tori in the same homology class, Trans. Amer. Math. Soc. 356 (2004), no. 9, 3739–3750. 10.1090/S0002-9947-03-03529-3Search in Google Scholar

[9] T. Etgü and B. D. Park, Homologous non-isotopic symplectic tori in a K3 surface, Commun. Contemp. Math. 7 (2005), no. 3, 325–340. 10.1142/S021919970500174XSearch in Google Scholar

[10] T. Etgü and B. D. Park, Symplectic tori in rational elliptic surfaces, Math. Ann. 334 (2006), no. 3, 679–691. 10.1007/s00208-005-0724-5Search in Google Scholar

[11] J. B. Etnyre, On symplectic fillings, Algebr. Geom. Topol. 4 (2004), 73–80. 10.2140/agt.2004.4.73Search in Google Scholar

[12] R. Fintushel and R. J. Stern, Rational blowdowns of smooth 4-manifolds, J. Differential Geom. 46 (1997), no. 2, 181–235. 10.4310/jdg/1214459932Search in Google Scholar

[13] R. Fintushel and R. J. Stern, Symplectic surfaces in a fixed homology class, J. Differential Geom. 52 (1999), no. 2, 203–222. 10.4310/jdg/1214425276Search in Google Scholar

[14] R. E. Gompf, A new construction of symplectic manifolds, Ann. of Math. (2) 142 (1995), no. 3, 527–595. 10.2307/2118554Search in Google Scholar

[15] B. Harbourne, Global aspects of the geometry of surfaces, Ann. Univ. Paedagog. Crac. Stud. Math. 11 (2010), 5–41. Search in Google Scholar

[16] Y. Karshon, L. Kessler and M. Pinsonnault, Symplectic blowups of the complex projective plane and counting toric actions, preprint (2012), www.utm.utoronto.ca/~karshony/papers/algorithm.121221-clean.pdf. Search in Google Scholar

[17] Y. Lee and J. Park, A simply connected surface of general type with pg=0 and K2=2, Invent. Math. 170 (2007), no. 3, 483–505. 10.1007/s00222-007-0069-7Search in Google Scholar

[18] B.-H. Li, Representing nonnegative homology classes of ℂ⁢P2⁢#⁢n⁢ℂ⁢P2¯ by minimal genus smooth embeddings, Trans. Amer. Math. Soc. 352 (2000), no. 9, 4155–4169. 10.1090/S0002-9947-99-02422-8Search in Google Scholar

[19] B.-H. Li and T.-J. Li, Symplectic genus, minimal genus and diffeomorphisms, Asian J. Math. 6 (2002), no. 1, 123–144. 10.4310/AJM.2002.v6.n1.a7Search in Google Scholar

[20] B.-H. Li and T.-J. Li, Smooth minimal genera for small negative classes in ℂ⁢P2⁢#⁢n⁢ℂ⁢P¯2 with n≤9, Topology Appl. 132 (2003), no. 1, 1–15. 10.1016/S0166-8641(02)00357-7Search in Google Scholar

[21] B.-H. Li and T.-J. Li, Circle-sum and minimal genus surfaces in ruled 4-manifolds, Proc. Amer. Math. Soc. 135 (2007), no. 11, 3745–3753. 10.1090/S0002-9939-07-08954-XSearch in Google Scholar

[22] T.-J. Li, Smoothly embedded spheres in symplectic 4-manifolds, Proc. Amer. Math. Soc. 127 (1999), no. 2, 609–613. 10.1090/S0002-9939-99-04457-3Search in Google Scholar

[23] T.-J. Li, Existence of symplectic surfaces, Geometry and topology of manifolds, Fields Inst. Commun. 47, American Mathematical Society, Providence (2005), 203–217. 10.1090/fic/047/12Search in Google Scholar

[24] T.-J. Li and A.-K. Liu, Symplectic structure on ruled surfaces and a generalized adjunction formula, Math. Res. Lett. 2 (1995), no. 4, 453–471. 10.4310/MRL.1995.v2.n4.a6Search in Google Scholar

[25] T.-J. Li and A.-K. Liu. Uniqueness of symplectic canonical class, surface cone and symplectic cone of 4-manifolds with b+=1, J. Differential Geom. 58 (2001), no. 2, 331–370. 10.4310/jdg/1090348329Search in Google Scholar

[26] T.-J. Li and M. Usher, Symplectic forms and surfaces of negative square, J. Symplectic Geom. 4 (2006), no. 1, 71–91. 10.4310/JSG.2006.v4.n1.a4Search in Google Scholar

[27] T.-J. Li and W. Wu, Lagrangian spheres, symplectic surfaces and the symplectic mapping class group, Geom. Topol. 16 (2012), no. 2, 1121–1169. 10.2140/gt.2012.16.1121Search in Google Scholar

[28] T.-J. Li and W. Zhang, Additivity and relative Kodaira dimension, Geometric analysis, no. 2, Adv. Lectures Math. 18, International Press, Somerville (2011), 103–135. Search in Google Scholar

[29] D. McDuff, From symplectic deformation to isotopy, Topics in symplectic 4-manifolds (Irvine 1996), First Int. Press Lect. Ser. 1, International Press, Cambridge (1998), 85–99. Search in Google Scholar

[30] D. McDuff and E. Opshtein, Nongeneric J-holomorphic curves and singular inflation, preprint (2013), http://arxiv.org/abs/1309.6425. Search in Google Scholar

[31] D. McDuff and L. Polterovich, Symplectic packings and algebraic geometry, with an appendix by Y. Karshon, Invent. Math. 115 (1994), no. 3, 405–434. 10.1007/BF01231766Search in Google Scholar

[32] H. Ohta and K. Ono, Simple singularities and symplectic fillings, J. Differential Geom. 69 (2005), no. 1, 117–142. 10.4310/jdg/1121540338Search in Google Scholar

[33] D. Ruberman, The minimal genus of an embedded surface of non-negative square in a rational surface, Turkish J. Math. 20 (1996), no. 1, 129–133. Search in Google Scholar

[34] V. Shevchishin, Secondary Stiefel–Whitney class and diffeomorphisms of rational and ruled symplectic 4-manifolds, preprint (2009), http://arxiv.org/abs/0904.0283. Search in Google Scholar

[35] I. Smith and R. Thomas, Symplectic surgeries from singularities, Turkish J. Math. 27 (2003), no. 1, 231–250. Search in Google Scholar

[36] A. I. Stipsicz, Z. Szabo and J. Wahl, Rational blowdowns and smoothings of surface singularities, J. Topol. 1 (2008), no. 2, 477–517. 10.1112/jtopol/jtn009Search in Google Scholar

[37] M. Symington, Symplectic rational blowdowns, J. Differential Geom. 50 (1998), no. 3, 505–518. 10.4310/jdg/1214424968Search in Google Scholar

[38] M. Symington, Generalized symplectic rational blowdowns, Algebr. Geom. Topol. 1 (2001), 503–518. 10.2140/agt.2001.1.503Search in Google Scholar

[39] C. H. Taubes, The Seiberg–Witten and Gromov invariants, Math. Res. Lett. 2 (1995), no. 2, 221–238. 10.4310/MRL.1995.v2.n2.a10Search in Google Scholar

[40] C. H. Taubes, Counting pseudo-holomorphic submanifolds in dimension 4, Seiberg–Witten and Gromov invariants for symplectic 4-manifolds, First Int. Press Lect. Ser. 2, International Press, Somerville (2000), 99–161. 10.4310/jdg/1214459411Search in Google Scholar

[41] C. H. Taubes, Seiberg–Witten and Gromov invariants for symplectic 4-manifolds, First Int. Press Lect. Ser. 2, International Press, Somerville 2000. Search in Google Scholar

[42] W. Wu, Exact Lagrangians in An-singularities, Math. Ann. 359 (2014), no. 1–2, 153–168. 10.1007/s00208-013-0993-3Search in Google Scholar