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arXiv · 1111.3841

Cohomology theories on locally conformal symplectic manifolds

Hông Vân Lê·Jiři Vanžura
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Abstract

In this note we introduce primitive cohomology groups of locally conformal symplectic manifolds $(M^{2n}, ω, θ)$. We study the relation between the primitive cohomology groups and the Lichnerowicz-Novikov cohomology groups of $(M^{2n}, ω, θ)$, using and extending the technique of spectral sequences developed by Di Pietro and Vinogradov for symplectic manifolds. We discuss related results by many peoples, e.g. Bouche, Lychagin, Rumin, Tseng-Yau, in light of our spectral sequences. We calculate the primitive cohomology groups of a $(2n+2)$-dimensional locally conformal symplectic nilmanifold as well as those of a l.c.s. solvmanifold. We show that the l.c.s. solvmanifold is a mapping torus of a contactomorphism, which is not isotopic to the identity.

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Hông Vân Lê, Jiři Vanžura. 2013-10-16. Cohomology theories on locally conformal symplectic manifolds. https://doi.org/10.4310/ajm.2015.v19.n1.a3

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