Geodesic
Exactly fillable contact structures without Stein fillings
Bowden, Jonathan1
1Mathematisches Institut, Universität Augsburg, Universitätsstrasse 14, 86159 Augsburg, Germany, Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53129 Bonn, Germany
Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1803-1810
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We give examples of contact structures which admit exact symplectic fillings, but no Stein fillings, answering a question of Ghiggini.

DOI : 10.2140/agt.2012.12.1803
Keywords: Stein filling, Symplectic filling, Contact topology, Symplectic topology

Bowden, Jonathan  1

1 Mathematisches Institut, Universität Augsburg, Universitätsstrasse 14, 86159 Augsburg, Germany, Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53129 Bonn, Germany 
@article{10_2140_agt_2012_12_1803,
     author = {Bowden, Jonathan},
     title = {Exactly fillable contact structures without {Stein} fillings},
     journal = {Algebraic and Geometric Topology},
     pages = {1803--1810},
     year = {2012},
     volume = {12},
     number = {3},
     doi = {10.2140/agt.2012.12.1803},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.1803/}
}
TY  - JOUR
AU  - Bowden, Jonathan
TI  - Exactly fillable contact structures without Stein fillings
JO  - Algebraic and Geometric Topology
PY  - 2012
SP  - 1803
EP  - 1810
VL  - 12
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.1803/
DO  - 10.2140/agt.2012.12.1803
ID  - 10_2140_agt_2012_12_1803
ER  - 
%0 Journal Article
%A Bowden, Jonathan
%T Exactly fillable contact structures without Stein fillings
%J Algebraic and Geometric Topology
%D 2012
%P 1803-1810
%V 12
%N 3
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.1803/
%R 10.2140/agt.2012.12.1803
%F 10_2140_agt_2012_12_1803
Bowden, Jonathan. Exactly fillable contact structures without Stein fillings. Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1803-1810. doi: 10.2140/agt.2012.12.1803

[1] K Cieliebak, Y Eliashberg, From Stein to Weinstein and Back: Symplectic geometry of affine complex manifolds, Colloquium Publications 59, Amer. Math. Soc. (2012)

[2] V Colin, Chirurgies d'indice un et isotopies de sphères dans les variétés de contact tendues, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 659

[3] Y Eliashberg, Filling by holomorphic discs and its applications, from: "Geometry of low-dimensional manifolds, 2 (Durham, 1989)", London Math. Soc. Lecture Note Ser. 151, Cambridge Univ. Press (1990) 45

[4] Y Eliashberg, Unique holomorphically fillable contact structure on the 3–torus, Internat. Math. Res. Notices (1996) 77

[5] J B Etnyre, K Honda, Tight contact structures with no symplectic fillings, Invent. Math. 148 (2002) 609

[6] D T Gay, Four-dimensional symplectic cobordisms containing three-handles, Geom. Topol. 10 (2006) 1749

[7] H Geiges, Examples of symplectic 4–manifolds with disconnected boundary of contact type, Bull. London Math. Soc. 27 (1995) 278

[8] P Ghiggini, Strongly fillable contact 3–manifolds without Stein fillings, Geom. Topol. 9 (2005) 1677

[9] P Ghiggini, J Van Horn-Morris, Tight contact structures on the Brieskorn spheres $-\Sigma(2,3,6n{-}1)$ and contact invariants

[10] E Giroux, Structures de contact sur les variétés fibrées en cercles audessus d'une surface, Comment. Math. Helv. 76 (2001) 218

[11] K Honda, On the classification of tight contact structures II, J. Differential Geom. 55 (2000) 83

[12] P Lisca, A I Stipsicz, Contact Ozsváth–Szabó invariants and Giroux torsion, Algebr. Geom. Topol. 7 (2007) 1275

[13] P Massot, Geodesible contact structures on 3–manifolds, Geom. Topol. 12 (2008) 1729

[14] D Mcduff, Symplectic manifolds with contact type boundaries, Invent. Math. 103 (1991) 651

[15] Y Mitsumatsu, Anosov flows and non–Stein symplectic manifolds, Ann. Inst. Fourier (Grenoble) 45 (1995) 1407

Cité par Sources :