We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness results and discuss a number of essential examples, including geometries related to special holonomy. For forms of degree four, multi-moment maps are guaranteed to exist and are unique when the symmetry group is (3,4)-trivial, meaning that the group is connected and the third and fourth Lie algebra Betti numbers vanish. We give a structural description of some classes of (3,4)-trivial algebras and provide a number of examples.
Geometriae Dedicata, 2013, Vol 165, Issue 1, p. 25-52
Moment map Multi-phase space Hamiltonian action Special holonomy Lie algebra cohomology EXCEPTIONAL HOLONOMY HOMOGENEOUS SPACES KILLING SPINORS GEOMETRY MANIFOLDS METRICS G(2)-STRUCTURES HYPERKAHLER SYMMETRY ALGEBRAS