We show that the dω-cohomology is isomorphic to a conformally invariant usual de Rham cohomology of an appropriate cover. We also prove a Moser theorem for locally conformal symplectic (lcs) forms. We point out a connection between lcs geometry and contact geometry. Finally, we show the connections between first kind, second kind, essential, inessential, local, and global conformal symplectic structures through several invariants.
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