%0 Journal Article
%T Cohomology theories on locally conformal symplectic manifolds
%A H£¿ng Van L¨º
%A Ji£¿i Van£¿ura
%J Mathematics
%D 2011
%I arXiv
%R 10.4310/AJM.2015.v19.n1.a3
%X In this note we introduce primitive cohomology groups of locally conformal symplectic manifolds $(M^{2n}, \omega, \theta)$. We study the relation between the primitive cohomology groups and the Lichnerowicz-Novikov cohomology groups of $(M^{2n}, \omega, \theta)$, 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.
%U http://arxiv.org/abs/1111.3841v4