On prolongations of contact manifolds

Details On prolongations of contact manifolds On prolongations of contact manifolds

2011-07-29

arxiv.org/abs/1107.5884v2

Mathematics

Symplectic Geometry

8 pages; incorporated changes proposed by the referee, reorganized slightly, exposition improved

Scientific paper

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 determine the Engel structure we additionally have to fix a class in the first cohomology of $M$.

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