Multi-moment maps
Copyright policy )Multi-moment maps
We introduce a notion of moment map adapted to actions of Lie groups that preserve a closed three-form. We show existence of our multi-moment maps in many circumstances, including mild topological assumptions on the underlying manifold. Such maps are also shown to exist for all groups whose second and third Lie algebra Betti numbers are zero. We show that these form a special class of solvable Lie groups and provide a structural characterisation. We provide many examples of multi-moment maps for different geometries and use them to describe manifolds with holonomy contained in G_2 preserved by a two-torus symmetry in terms of tri-symplectic geometry of four-manifolds.
27 pages
- Aarhus University Denmark
- King's College London United Kingdom
- Aarhus University Denmark
- University of Southern Denmark Denmark
Issues of holonomy in differential geometry, Mathematics - Differential Geometry, High Energy Physics - Theory, Mathematics(all), FOS: Physical sciences, Global differential geometry of Hermitian and Kählerian manifolds, moment map, Momentum maps; symplectic reduction, solvable Lie algebra, General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Special holonomy, Nilpotent and solvable Lie groups, Solvable Lie algebra, three-form, Differential geometry of homogeneous manifolds, Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics, Differential Geometry (math.DG), High Energy Physics - Theory (hep-th), Moment map, special holonomy, Three-form, 53C15 (Primary) 22E25, 53C29, 53C30, 53C55, 53D20, 70G45 (Secondary)
Issues of holonomy in differential geometry, Mathematics - Differential Geometry, High Energy Physics - Theory, Mathematics(all), FOS: Physical sciences, Global differential geometry of Hermitian and Kählerian manifolds, moment map, Momentum maps; symplectic reduction, solvable Lie algebra, General geometric structures on manifolds (almost complex, almost product structures, etc.), FOS: Mathematics, Special holonomy, Nilpotent and solvable Lie groups, Solvable Lie algebra, three-form, Differential geometry of homogeneous manifolds, Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics, Differential Geometry (math.DG), High Energy Physics - Theory (hep-th), Moment map, special holonomy, Three-form, 53C15 (Primary) 22E25, 53C29, 53C30, 53C55, 53D20, 70G45 (Secondary)
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