On prolongations of contact manifolds

Klukas, Mirko; Sahamie, Bijan

doi:10.1090/S0002-9939-2013-11777-6

On prolongations of contact manifolds
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by Mirko Klukas and Bijan Sahamie PDF

Proc. Amer. Math. Soc. 141 (2013), 3257-3263 Request permission

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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