In 2002, Giroux showed that every contact structure had a corresponding open book decomposition. This was the converse to a previous construction of Thurston and Winkelnkemper, and made open books a vital tool in the study of contact three-manifolds. We extend these results to contact orbifolds, i.e. spaces that are locally diffeomorphic to the quotient of a contact manifold and a compatible finite group action. This involves adapting some of the main concepts and constructions of three dimensional contact geometry to the orbifold setting.
Identifer | oai:union.ndltd.org:UMASS/oai:scholarworks.umass.edu:open_access_dissertations-1806 |
Date | 01 September 2013 |
Creators | Herr, Daniel |
Publisher | ScholarWorks@UMass Amherst |
Source Sets | University of Massachusetts, Amherst |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Open Access Dissertations |
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