Closed forms and multi-moment maps

2011/10/29 by Thomas Bruun Madsen, Andrew Swann · 1 citation
Mathematics · Physics and Astronomy · #math.DG #hep-th #msc:53C15 #msc:22E25 #msc:53C29 #msc:53C30 #msc:53C55 #msc:53D20 #msc:70G45

paper · pdf · doi:10.1007/s10711-012-9783-4

published as Geom. Dedicata 165, Issue 1 (2013), 25-52 · 36 pages

arxiv created 2011/10/29 · arxiv updated 2014/09/16

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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• Reduction of relative multisymplectic manifolds
• Relative homotopy moment maps

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