定向旋回轨道褶皱的分类结果及切触结构
A classification result and contact structures in oriented cyclic orbifold
摘要：
证明了每个定向紧循环$3$ -orbifold都有切触结构.网络上还有另一个由Daniel Herr在他上传的论文中提出的证明，它依赖于开卷分解，我们的证明与之无关。定义了定向紧致循环3-orbifold上的过扭切触结构、紧切触结构和Lutz扭。我们证明了用我们的方法接触的有向紧致循环$3$ -orbifold中的每一个切触结构都同伦于一个过扭曲结构，其中过扭曲盘与orbifold的奇异轨迹相交。我们提出Eliashberg的过扭曲的切触结构的环状$3$ -orbifolds作为一个开放的问题。在证明上述结果的过程中，我们证明了一个在文献中未曾见到的紧致定向循环3轨道折叠的分类结果。
英文摘要：
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 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 orbifold. We pose Eliashberg's like characterization of overtwisted contact structures of cyclic $3$-orbifolds as an open problem. 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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