Abstract
OPEN BOOKS ON CONTACT THREE ORBIFOLDS SEPTEMBER 2013 DANIEL HERR B.A., OBERLIN COLLEGE Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Weimin Chen In 2002, Giroux showed that every contact structure has 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.
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