Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-07T12:42:42.183Z Has data issue: false hasContentIssue false
  • English
  • Français

Symplectic fillings of links of quotient surface singularities

Published online by Cambridge University Press:  11 January 2016

Mohan Bhupal  and
Kaoru Ono
Mohan Bhupal
Affiliation:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey, bhupal@metu.edu.tr
Kaoru Ono
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan, ono@kurims.kyoto-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We study symplectic deformation types of minimal symplectic fillings of links of quotient surface singularities. In particular, there are only finitely many symplectic deformation types for each quotient surface singularity.

Keywords

53D3557R1732S25

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 207 , September 2012 , pp. 1 - 45
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2012

References

[1] Bhupal, M., On symplectic fillings of links of rational surface singularities with reduced fundamental cycle, Nagoya Math. J. 175 (2004), 51–57.CrossRefGoogle Scholar
[2] Brieskorn, E., Rationale singularitäten komplexer flächen, Invent. Math. 4 (1968), 336–358.CrossRefGoogle Scholar
[3] Giroux, E., Structures de contact en dimension trois et bifurcations des feuilletages de surfaces, Invent. Math. 141 (2000), 615–689.CrossRefGoogle Scholar
[4] Eliashberg, Y., “Filling by holomorphic discs and its applications” in Geometry of Low-dimensional Manifolds, 2 (Durham, England, 1989), London Math. Soc. Lecture Notes Ser. 151, Cambridge University Press, Cambridge, 1990, 45–67.Google Scholar
[5] Godinho, L., Blowing up symplectic orbifolds, Ann. Global Anal. Geom. 20 (2001), 117–162.CrossRefGoogle Scholar
[6] Gromov, M., Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307–347.CrossRefGoogle Scholar
[7] Honda, K., On the classification of tight contact structures, I, Geom. Topol. 4 (2000), 309–368.CrossRefGoogle Scholar
[8] Kanda, Y., The monopole equation and J-holomorphic curves on weakly convex almost K ähler 4-manifolds, Trans. Amer. Math. Soc., no. 6, 353 (2001), 2215–2243.CrossRefGoogle Scholar
[9] Lalonde, F. and McDuff, D., The classification of ruled symplectic 4-manifolds, Math. Res. Lett. 3 (1996), 769–778.CrossRefGoogle Scholar
[10] Lisca, P., Symplectic fillings and positive scalar curvature, Geom. Topol. 2 (1998), 103–116.CrossRefGoogle Scholar
[11] Lisca, P., On lens spaces and their symplectic fillings, Math. Res. Lett. 11 (2004), 13–22.CrossRefGoogle Scholar
[12] Lisca, P., On symplectic fillings of lens spaces, Trans. Amer. Math. Soc., no. 2, 360 (2008), 765–799.CrossRefGoogle Scholar
[13] Liu, A., Some new applications of general wall-crossing formula, Gompf’s conjecture and its applications, Math. Res. Lett. 3 (1996), 569–585.CrossRefGoogle Scholar
[14] McCarthy, J. D. and Wolfson, J. G., Symplectic gluing along hypersurfaces and resolution of isolated orbifold singularities, Invent. Math. 119 (1995), 129–154.CrossRefGoogle Scholar
[15] McDuff, M., The structure of rational and ruled symplectic 4-manifolds, J. Amer. Math. Soc. 3 (1990), 679–712; erratum, J. Amer. Math. Soc. 5 (1992), 987–988.CrossRefGoogle Scholar
[16] McDuff, M., Symplectic manifolds with contact type boundaries, Invent. Math. 103 (1991), 651–671.CrossRefGoogle Scholar
[17] Ohta, H. and Ono, K., Notes on symplectic 4-manifolds with b+ 2 = 1, II, Internat. J. Math. 7 (1996), 755–770.CrossRefGoogle Scholar
[18] Ohta, H. and Ono, K., Simple singularities and topology of symplectically filling 4-manifolds, Comment. Math. Helv. 74 (1999), 575–590.CrossRefGoogle Scholar
[19] Ohta, H. and Ono, K., Symplectic fillings of the link of simple elliptic singularities, J. Reine Angew. Math. 565 (2003), 183–205.Google Scholar
[20] Ohta, H. and Ono, K., Simple singularities and symplectic fillings, J. Differential Geom. 69 (2005), 1–42.CrossRefGoogle Scholar
[21] Ohta, H. and Ono, K., Symplectic 4-manifolds containing singular rational curves with (2,3)-cusp, Sémin. Congr. 10 (2005), 233–241.Google Scholar
[22] Riemenschneider, O., Die Invarianten der endlichen Untergruppen von GL(2,C), Math Z. 153 (1977), 37–50.Google Scholar
[23] Saito, K., A new relation among Cartan matrix and Coxeter matrix, J. Algebra 105 (1987), 149–158.CrossRefGoogle Scholar
[24] Taubes, C. H., Seiberg Witten and Gromov Invariants for Symplectic 4-Manifolds, International Press, Somerville, MA, 2000.Google Scholar