Geodesic
Transverse contact structures on Seifert 3–manifolds
Lisca, Paolo1 ; Matić, Gordana2
1Dipartimento di Matematica “L Tonelli”, Università di Pisa, I-56127 Pisa, Italy
2Department of Mathematics, University of Georgia, Athens GA 30602, USA
Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 1125-1144
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We characterize the oriented Seifert–fibered three–manifolds which admit positive, transverse contact structures.

DOI : 10.2140/agt.2004.4.1125
Keywords: transverse contact structures, Seifert three–manifolds

Lisca, Paolo  1   ; Matić, Gordana  2

1 Dipartimento di Matematica “L Tonelli”, Università di Pisa, I-56127 Pisa, Italy
2 Department of Mathematics, University of Georgia, Athens GA 30602, USA 
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Lisca, Paolo; Matić, Gordana. Transverse contact structures on Seifert 3–manifolds. Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 1125-1144. doi: 10.2140/agt.2004.4.1125

[1] D Eisenbud, U Hirsch, W Neumann, Transverse foliations of Seifert bundles and self-homeomorphism of the circle, Comment. Math. Helv. 56 (1981) 638

[2] 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

[3] Y Eliashberg, A few remarks about symplectic filling, Geom. Topol. 8 (2004) 277

[4] Y M Eliashberg, W P Thurston, Confoliations, University Lecture Series 13, American Mathematical Society (1998)

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

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

[7] K Honda, Confoliations transverse to vector fields, preprint

[8] J Hempel, 3–Manifolds, Ann. of Math. Studies 86, Princeton University Press (1976)

[9] M Jankins, W Neumann, Homomorphisms of Fuchsian groups to $\mathrm{PSL}(2,\mathbb{R})$, Comment. Math. Helv. 60 (1985) 480

[10] M Jankins, W D Neumann, Rotation numbers of products of circle homeomorphisms, Math. Ann. 271 (1985) 381

[11] P B Kronheimer, T S Mrowka, Monopoles and contact structures, Invent. Math. 130 (1997) 209

[12] J Milnor, On the existence of a connection with curvature zero, Comment. Math. Helv. 32 (1958) 215

[13] J D Mccarthy, J G Wolfson, Symplectic gluing along hypersurfaces and resolution of isolated orbifold singularities, Invent. Math. 119 (1995) 129

[14] R Naimi, Foliations transverse to fibers of Seifert manifolds, Comment. Math. Helv. 69 (1994) 155

[15] W D Neumann, F Raymond, Seifert manifolds, plumbing, $\mu $–invariant and orientation reversing maps, from: "Algebraic and geometric topology (Proc. Sympos., Univ. California, Santa Barbara, Calif., 1977)", Lecture Notes in Math. 664, Springer (1978) 163

[16] P Orlik, Seifert manifolds, Lecture Notes in Mathematics 291, Springer (1972)

[17] P Ozsváth, Z Szabó, The symplectic Thom conjecture, Ann. of Math. $(2)$ 151 (2000) 93

[18] O Riemenschneider, Deformationen von Quotientensingularitäten (nach zyklischen Gruppen), Math. Ann. 209 (1974) 211

[19] A Sato, T Tsuboi, Contact structures on closed manifolds fibered by the circles, Mem. Inst. Sci. Tech. Meiji Univ. 33 (1994) 41

[20] J W Wood, Bundles with totally disconnected structure group, Comment. Math. Helv. 46 (1971) 257

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