# The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry

Complex Manifolds (2017)

- Volume: 4, Issue: 1, page 183-199
- ISSN: 2300-7443

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topAndrea Seppi. "The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry." Complex Manifolds 4.1 (2017): 183-199. <http://eudml.org/doc/288442>.

@article{AndreaSeppi2017,

abstract = {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’).},

author = {Andrea Seppi},

journal = {Complex Manifolds},

language = {eng},

number = {1},

pages = {183-199},

title = {The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry},

url = {http://eudml.org/doc/288442},

volume = {4},

year = {2017},

}

TY - JOUR

AU - Andrea Seppi

TI - The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry

JO - Complex Manifolds

PY - 2017

VL - 4

IS - 1

SP - 183

EP - 199

AB - 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’).

LA - eng

UR - http://eudml.org/doc/288442

ER -

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