Abstract
We apply spectral sequences to derive both an obstruction to the existence of n 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 × S 1 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 M .
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