A cohomological framework for homotopy moment maps

Abstract

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].

18 pages, final version. Added reference [16] by L. Ryvkin and T. Wurzbacher, who obtain independently results similar to ours putting an emphasis on the differential geometry of multisymplectic forms

References in corpus (3)

• L-infinity algebras of local observables from higher prequantum bundles
• Erratum to: "A Proof of Tsygan's Formality Conjecture for an Arbitrary Smooth Manifold"
• Products of multisymplectic manifolds and homotopy moment maps

Cited by in corpus (9)

• Noether's Theorem in Multisymplectic Geometry
• Existence and Uniqueness of Weak Homotopy Moment Maps
• Conserved quantities on multisymplectic manifolds
• Products of multisymplectic manifolds and homotopy moment maps
• Graded Poisson and Graded Dirac structures
• Weak Moment Maps in Multisymplectic Geometry
• A hydrodynamical homotopy co-momentum map and a multisymplectic interpretation of higher order linking numbers
• Multisymplectic actions of compact Lie groups on spheres
• Reduction of $L_{\infty }$-Algebras of Observables on Multisymplectic Manifolds