Abstract
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.
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Madsen, T.B., Swann, A. Closed forms and multi-moment maps. Geom Dedicata 165, 25–52 (2013). https://doi.org/10.1007/s10711-012-9783-4
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DOI: https://doi.org/10.1007/s10711-012-9783-4