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arXiv · 1110.6541

Closed forms and multi-moment maps

Thomas Bruun Madsen·Andrew Swann
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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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Thomas Bruun Madsen, Andrew Swann. 2011-10-29. Closed forms and multi-moment maps. https://doi.org/10.1007/s10711-012-9783-4

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