On characteristic classes of Q-manifolds
  We define the notion of characteristic classes for supermanifolds endowed with a homological vector field $Q$. These take values in the cohomology of the Lie derivative operator $L_Q$ acting on arbitrary tensor fields. We formulate a classification theorem for intrinsic characteristic classes and give their explicit description. 
S.L. Lyakhovich, E.A. Mosman and A.A. Sharapov