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We prove every oriented compact cyclic $3$-orbifold has a contact structure. There is another proof in the web by Daniel Herr in his uploaded thesis which depends on open book decompositions, ours is independent of that. We define overtwisted contact structures, tight contact structures and Lutz twist on oriented compact cyclic 3-orbifolds. We show that every contact structure in an oriented compact cyclic $3$-orbifold contactified by our method is homotopic to an overtwisted structure with the overtwisted disc intersecting the singular locus of the orbifolds. In course of proving the above results we prove a classification result for compact oriented cyclic-3 orbifolds which has not been seen by us in literature before.
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참고문헌 (4)
참고문헌 신청
A. Adem / 2007 / Orbifolds and stringy topology;Cambridge Tracts in Mathematics / Cambridge University Press :171
Y. Eliashberg / 1989 / Classification of overtwisted contact structures on 3-manifolds / Invent. Math. 98(3):623~637
H. Geiges / 2008 / An introduction to contact topology;Cambridge Studies in Advanced Mathematics / Cambridge University Press :109
D. Herr / Open books in contact 3 orbifolds
Y. Eliashberg / 1989 / Classification of overtwisted contact structures on 3-manifolds / Invent. Math. 98(3):623~637
H. Geiges / 2008 / An introduction to contact topology;Cambridge Studies in Advanced Mathematics / Cambridge University Press :109
D. Herr / Open books in contact 3 orbifolds
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