For a local Lie group M we define cohomology classes [is an obstruction to globalizability and give an example where [w1] = 0. We also show that [w3] coincides with Godbillon-Vey class in a particular case. These classes are secondary as they emerge when curvature vanishes.

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Abstract. In this work, we show that an autonomous dynamical system defined by a nonvanishing vector field on an orientable three-dimensional manifold is globally bi-Hamiltonian if and only if the first Chern class of the normal bundle of the given vector field vanishes. Furthermore, the bi-Hamiltonian structure is globally compatible if and only if the Bott class of the complex codimension one foliation defined by the given vector field vanishes.