DOI QR코드

DOI QR Code

A CLASSIFICATION RESULT AND CONTACT STRUCTURES IN ORIENTED CYCLIC 3-ORBIFOLDS

  • Received : 2017.02.27
  • Accepted : 2017.09.08
  • Published : 2018.01.31

Abstract

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.

Keywords

References

  1. A. Adem, J. Leida, and Y. Ruan, Orbifolds and stringy topology, Cambridge Tracts in Mathematics, 171, Cambridge University Press, Cambridge, 2007.
  2. Y. Eliashberg, Classification of overtwisted contact structures on 3-manifolds, Invent. Math. 98 (1989), no. 3, 623-637. https://doi.org/10.1007/BF01393840
  3. H. Geiges, An introduction to contact topology, Cambridge Studies in Advanced Mathematics, 109, Cambridge University Press, Cambridge, 2008.
  4. D. Herr Open books in contact 3 orbifolds, Dissertations and Theses University of Massachusetts - Amherst ScholarWorks@UMass Amherst.