Closed forms and multi-moment maps

Preprint number: CP3-Origins-2011-37 and DIAS-2011-29
Authors: Thomas Bruun Madsen (CP3-Origins) and Andrew Swann (CP3-Origins)
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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.