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

Andrea 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 -