2012
DOI: 10.1007/s10711-012-9783-4
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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… Show more

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Cited by 38 publications
(44 citation statements)
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“…Also notice that the n-th component of a weak moment map is precisely the moment map introduced by Madsen and Swann in [6] and [7].…”
Section: Weak Homotopy Moment Mapsmentioning
confidence: 85%
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“…Also notice that the n-th component of a weak moment map is precisely the moment map introduced by Madsen and Swann in [6] and [7].…”
Section: Weak Homotopy Moment Mapsmentioning
confidence: 85%
“…Notice that for the case n = k, it is always true that H 0 (g, Ω n−k cl ) = 0 since any-non zero constant function is closed. Hence Theorem 5.6 gives a generalization of Theorems 3.5 and 3.14 of [6] and [7] respectively. Moreover, by taking n = k = 1, we see that we are obtaining a generalization from symplectic geometry.…”
Section: Proof By Linearity It Suffices To Consider Decomposablementioning
confidence: 88%
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“…It is important to compare other generalizations of a moment map theory to a multisymplectic manifold such as Madsen-Swann's multimoment map on the n-th Lie kernel [20,21], a homotopy moment map [11], and a weak moment map [13].…”
Section: Discussion and Outlookmentioning
confidence: 99%
“…Instead, we need to restrict our attention to multivector fields in the Lie kernel, which we defined in Definition 2.8. We quickly recall this definition and some terminology and notation introduced in [12].…”
Section: Classical Multisymplectic Momentum and Position Formsmentioning
confidence: 99%