×
Lecuona, Ana G.; Lisca, Paolo

Stein fillable Seifert fibered 3-manifolds. (English) Zbl 1213.57029

Algebr. Geom. Topol. 11, No. 2, 625-642 (2011).
Authors’ abstract: In this paper the authors characterize the closed, oriented, Seifert fibered 3-manifolds which are oriented boundaries of Stein manifolds. They also show that the existence of Stein fillings is equivalent to the existence of symplectic fillings for this class of 3-manifolds.
Reviewer: Zhigang Han (Millersville)

Cited in 12 Documents

MSC:

57R17 Symplectic and contact topology in high or arbitrary dimension
53D10 Contact manifolds (general theory)

Keywords:

Seifert fibered 3-manifold; Stein filling; symplectic filling; positive open book
PDF BibTeX XML Cite
\textit{A. G. Lecuona} and \textit{P. Lisca}, Algebr. Geom. Topol. 11, No. 2, 625--642 (2011; Zbl 1213.57029)
Full Text: DOI arXiv

References:

[1] S K Donaldson, The orientation of Yang-Mills moduli spaces and \(4\)-manifold topology, J. Differential Geom. 26 (1987) 397 · Zbl 0683.57005
[2] D Eisenbud, U Hirsch, W Neumann, Transverse foliations of Seifert bundles and self-homeomorphism of the circle, Comment. Math. Helv. 56 (1981) 638 · Zbl 0516.57015
[3] Y Eliashberg, Filling by holomorphic discs and its applications (editors S K Donaldson, C B Thomas), London Math. Soc. Lecture Note Ser. 151, Cambridge Univ. Press (1990) 45 · Zbl 0731.53036
[4] Y Eliashberg, Topological characterization of Stein manifolds of dimension \(> 2\), Internat. J. Math. 1 (1990) 29 · Zbl 0699.58002
[5] J B Etnyre, Introductory lectures on contact geometry (editors G Matić, C McCrory), Proc. Sympos. Pure Math. 71, Amer. Math. Soc. (2003) 81 · Zbl 1045.57012
[6] H Geiges, An introduction to contact topology, Cambridge Studies in Advanced Math. 109, Cambridge Univ. Press (2008) · Zbl 1153.53002
[7] P Ghiggini, Strongly fillable contact \(3\)-manifolds without Stein fillings, Geom. Topol. 9 (2005) 1677 · Zbl 1091.57018
[8] P Ghiggini, P Lisca, A I Stipsicz, Tight contact structures on some small Seifert fibered \(3\)-manifolds, Amer. J. Math. 129 (2007) 1403 · Zbl 1175.57018
[9] R E Gompf, Handlebody construction of Stein surfaces, Ann. of Math. \((2)\) 148 (1998) 619 · Zbl 0919.57012
[10] M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 · Zbl 0592.53025
[11] M Jankins, W D Neumann, Rotation numbers of products of circle homeomorphisms, Math. Ann. 271 (1985) 381 · Zbl 0543.57019
[12] P Lisca, Symplectic fillings and positive scalar curvature, Geom. Topol. 2 (1998) 103 · Zbl 0942.53050
[13] P Lisca, Lens spaces, rational balls and the ribbon conjecture, Geom. Topol. 11 (2007) 429 · Zbl 1185.57006
[14] P Lisca, G Matić, Transverse contact structures on Seifert \(3\)-manifolds, Algebr. Geom. Topol. 4 (2004) 1125 · Zbl 1070.57013
[15] P Lisca, A I Stipsicz, An infinite family of tight, not semi-fillable contact three-manifolds, Geom. Topol. 7 (2003) 1055 · Zbl 1127.57302
[16] P Lisca, A I Stipsicz, Ozsváth-Szabó invariants and tight contact three-manifolds. I, Geom. Topol. 8 (2004) 925 · Zbl 1059.57017
[17] P Lisca, A I Stipsicz, Tight, not semi-fillable contact circle bundles, Math. Ann. 328 (2004) 285 · Zbl 1046.57018
[18] P Lisca, A I Stipsicz, Ozsváth-Szabó invariants and tight contact \(3\)- -manifolds. III, J. Symplectic Geom. 5 (2007) 357 · Zbl 1149.57037
[19] P Lisca, A I Stipsicz, Ozsváth-Szabó invariants and tight contact three-manifolds. II, J. Differential Geom. 75 (2007) 109 · Zbl 1112.57005
[20] P Lisca, A I Stipsicz, On the existence of tight contact structures on Seifert fibered \(3\)-manifolds, Duke Math. J. 148 (2009) 175 · Zbl 1233.57013
[21] A Loi, R Piergallini, Compact Stein surfaces with boundary as branched covers of \(B^4\), Invent. Math. 143 (2001) 325 · Zbl 0983.32027
[22] R Naimi, Foliations transverse to fibers of Seifert manifolds, Comment. Math. Helv. 69 (1994) 155 · Zbl 0797.55009
[23] W D Neumann, F Raymond, Seifert manifolds, plumbing, \(\mu \)-invariant and orientation reversing maps (editor K C Millett), Lecture Notes in Math. 664, Springer (1978) 163 · Zbl 0401.57018
[24] P Ozsváth, Z Szabó, Holomorphic disks and genus bounds, Geom. Topol. 8 (2004) 311 · Zbl 1056.57020
[25] P Ozsváth, Z Szabó, On knot Floer homology and lens space surgeries, Topology 44 (2005) 1281 · Zbl 1077.57012
[26] O Riemenschneider, Deformationen von Quotientensingularitäten (nach zyklischen Gruppen), Math. Ann. 209 (1974) 211 · Zbl 0275.32010
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.