The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry
Given a smooth spacelike surface ∑ of negative curvature in Anti-de Sitter space of dimension 3, invariant by a representation p: π1 (S) → PSL2ℝ x PSL2ℝ where S is a closed oriented surface of genus ≥ 2, a canonical construction associates to ∑ a diffeomorphism φ∑ of S. It turns out that φ∑ is a sym...
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De Gruyter
2017
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oai:doaj.org-article:d95346833bdd4a8aad6ccb53abd4a92f2021-12-02T16:36:59ZThe flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry2300-744310.1515/coma-2017-0013https://doaj.org/article/d95346833bdd4a8aad6ccb53abd4a92f2017-12-01T00:00:00Zhttps://doi.org/10.1515/coma-2017-0013https://doaj.org/toc/2300-7443Given a smooth spacelike surface ∑ of negative curvature in Anti-de Sitter space of dimension 3, invariant by a representation p: π1 (S) → PSL2ℝ x PSL2ℝ where S is a closed oriented surface of genus ≥ 2, a canonical construction associates to ∑ a diffeomorphism φ∑ of S. It turns out that φ∑ is a symplectomorphism for the area forms of the two hyperbolic metrics h and h' on S induced by the action of p on ℍ2 x ℍ2. Using an algebraic construction related to the flux homomorphism, we give a new proof of the fact that φ∑ is the composition of a Hamiltonian symplectomorphism of (S, h) and the unique minimal Lagrangian diffeomorphism from (S, h) to (S, h’).Seppi AndreaDe Gruyterarticle57m5053d0530f45MathematicsQA1-939ENComplex Manifolds, Vol 4, Iss 1, Pp 183-199 (2017) |
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57m50 53d05 30f45 Mathematics QA1-939 |
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57m50 53d05 30f45 Mathematics QA1-939 Seppi Andrea The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry |
| description |
Given a smooth spacelike surface ∑ of negative curvature in Anti-de Sitter space of dimension 3, invariant by a representation p: π1 (S) → PSL2ℝ x PSL2ℝ where S is a closed oriented surface of genus ≥ 2, a canonical construction associates to ∑ a diffeomorphism φ∑ of S. It turns out that φ∑ is a symplectomorphism for the area forms of the two hyperbolic metrics h and h' on S induced by the action of p on ℍ2 x ℍ2. Using an algebraic construction related to the flux homomorphism, we give a new proof of the fact that φ∑ is the composition of a Hamiltonian symplectomorphism of (S, h) and the unique minimal Lagrangian diffeomorphism from (S, h) to (S, h’). |
| format |
article |
| author |
Seppi Andrea |
| author_facet |
Seppi Andrea |
| author_sort |
Seppi Andrea |
| title |
The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry |
| title_short |
The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry |
| title_full |
The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry |
| title_fullStr |
The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry |
| title_full_unstemmed |
The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry |
| title_sort |
flux homomorphism on closed hyperbolic surfaces and anti-de sitter three-dimensional geometry |
| publisher |
De Gruyter |
| publishDate |
2017 |
| url |
https://doaj.org/article/d95346833bdd4a8aad6ccb53abd4a92f |
| work_keys_str_mv |
AT seppiandrea thefluxhomomorphismonclosedhyperbolicsurfacesandantidesitterthreedimensionalgeometry AT seppiandrea fluxhomomorphismonclosedhyperbolicsurfacesandantidesitterthreedimensionalgeometry |
| _version_ |
1718383661685932032 |