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arXiv · 1312.2712

Pushing down the Rumin complex to conformally symplectic quotients

Andreas Cap·Tomas Salac
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Abstract

Given a contact manifold $M_#$ together with a transversal infinitesimal automorphism $ξ$, we show that any local leaf space $M$ for the foliation determined by $ξ$ naturally carries a conformally symplectic (cs-) structure. Then we show that the Rumin complex on $M_#$ descends to a complex of differential operators on $M$, whose cohomology can be computed. Applying this construction locally, one obtains a complex intrinsically associated to any manifold endowed with a cs-structure, which recovers the generalization of the so-called Rumin-Seshadri complex to the conformally symplectic setting. The cohomology of this more general complex can be computed using the push-down construction.

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Andreas Cap, Tomas Salac. 2014-05-15. Pushing down the Rumin complex to conformally symplectic quotients. https://doi.org/10.1016/j.difgeo.2014.05.004

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