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We investigate the generic 3D topological field theory within AKSZ-BVframework. We use the Batalin-Vilkovisky (BV) formalism to construct explicitlycocycles of the Lie algebra of formal Hamiltonian vector fields and we arguethat the perturbative partition function gives rise to secondary characteristicclasses. We investigate a toy model which is an odd analogue of Chern-Simonstheory, and we give some explicit computation of two point functions and showthat its perturbation theory is identical to the Chern-Simons theory. We giveconcrete example of the homomorphism taking Lie algebra cocycles toQ-characteristic classes, and we reinterpreted the Rozansky-Witten model inthis light.

Odd Chern-Simons Theory, Lie Algebra Cohomology and Characteristic Classes