A cohomological framework for homotopy moment maps

International audienceGiven a Lie group acting on a manifold M preserving a closed n+1-form ω, the notion of homotopy moment map for this action was introduced in [FRZ], in terms of L∞-algebra morphisms. In this note we describe homotopy moment maps as coboundaries of a certain complex. This description simplifies greatly computations, and we use it to study various properties of homotopy moment maps: their relation to equivariant cohomology, their obstruction theory, how they induce new ones on mapping spaces, and their equivalences. The results we obtain extend some of the results of [FRZ]