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Article Dans Une Revue Journal of Geometry and Physics Année : 2015

A cohomological framework for homotopy moment maps

Camille Laurent-Gengoux
Marco Zambon
  • Fonction : Auteur

Résumé

Given a Lie group acting on a manifold $M$ preserving a closed $n+1$-form $\omega$, the notion of homotopy moment map for this action was introduced in Callies-Fregier-Rogers-Zambon [6], in terms of $L_{\infty}$-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 [6].

Dates et versions

hal-03174953 , version 1 (19-03-2021)

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Yaël Frégier, Camille Laurent-Gengoux, Marco Zambon. A cohomological framework for homotopy moment maps. Journal of Geometry and Physics, 2015, 97, pp.119-132. ⟨10.1016/j.geomphys.2015.07.010⟩. ⟨hal-03174953⟩

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