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Mathematics > Differential Geometry

arXiv:0710.0639 (math)
[Submitted on 2 Oct 2007 (v1), last revised 9 Dec 2008 (this version, v2)]

Title:Dirac geometry, quasi-Poisson actions and D/G-valued moment maps

Authors:Henrique Bursztyn, Marius Crainic
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Abstract: We study Dirac structures associated with Manin pairs (\d,\g) and give a Dirac geometric approach to Hamiltonian spaces with D/G-valued moment maps, originally introduced by Alekseev and Kosmann-Schwarzbach in terms of quasi-Poisson structures. We explain how these two distinct frameworks are related to each other, proving that they lead to isomorphic categories of Hamiltonian spaces. We stress the connection between the viewpoint of Dirac geometry and equivariant differential forms. The paper discusses various examples, including q-Hamiltonian spaces and Poisson-Lie group actions, explaining how presymplectic groupoids are related to the notion of "double" in each context.
Comments: 55 pages. v2: minor corrections, typos fixed; to appear in J. Differential Geometry
Subjects: Differential Geometry (math.DG); Symplectic Geometry (math.SG)
Cite as: arXiv:0710.0639 [math.DG]
  (or arXiv:0710.0639v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.0639

Submission history

From: Henrique Bursztyn [view email]
[v1] Tue, 2 Oct 2007 20:34:10 UTC (63 KB)
[v2] Tue, 9 Dec 2008 14:57:09 UTC (58 KB)
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