Closed forms and multi-moment maps

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.

36 pages

References in corpus (7)

• Multi-moment maps
• Special metric structures and closed forms
• IIB black hole horizons with five-form flux and KT geometry
• Reduction Procedures in Classical and Quantum Mechanics
• Spin(7)-manifolds with three-torus symmetry
• Half-flat structures on indecomposable Lie groups
• Homogeneous spaces, multi-moment maps and (2,3)-trivial algebras

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