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On prolongations of contact manifolds

Authors: Mirko Klukas and Bijan Sahamie
Journal: Proc. Amer. Math. Soc. 141 (2013), 3257-3263
MSC (2010): Primary 53D10
Published electronically: May 22, 2013
MathSciNet review: 3068978
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Abstract: We apply spectral sequences to derive both an obstruction to the existence of $ n$-fold prolongations and a topological classification. Prolongations have been used in the literature in an attempt to prove that every Engel structure on $ M\times \mathbb{S}^1$ with characteristic line field tangent to the fibers is determined by the contact structure induced on a cross section and the twisting of the Engel structure along the fibers. Our results show that this statement needs some modification: to classify the diffeomorphism type of the Engel structure, we additionally have to fix a class in the first cohomology of $ M$.

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Additional Information

Mirko Klukas
Affiliation: Mathematisches Institut der Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany

Bijan Sahamie
Affiliation: Mathematisches Institut der LMU München, Theresienstrasse 39, 80333 München, Germany
Address at time of publication: Stanford University, 450 Serra Mall, Building 380, Stanford, California 94305

Received by editor(s): August 5, 2011
Received by editor(s) in revised form: November 24, 2011
Published electronically: May 22, 2013
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2013 American Mathematical Society

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