Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2018; 33(1): 325-335

Online first article October 13, 2017      Printed January 31, 2018

https://doi.org/10.4134/CKMS.c170069

Copyright © The Korean Mathematical Society.

A classification result and contact structures in oriented cyclic 3-orbifolds

Saibal Ganguli

Chhatnag Road

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: contact structures, cyclic orbifolds, oriented, overtwisted structures, Lutz twist

MSC numbers: Primary 57R17, 57R18, 57R55; Secondary 53D10

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