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

• Autorzy: Andrea Seppi
• Języki publikacji: EN

Abstrakty

EN

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’).

Kategorie tematyczne

• 53D05: Symplectic manifolds, general
• 57M50: Geometric structures on low-dimensional manifolds
• 30F45: Conformal metrics (hyperbolic, Poincar\'e, distance functions)

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2017
• Tom: 4
• Numer: 1
• Strony: 183-199

Daty

wydano

2017-12-20

otrzymano

2017-10-05

zaakceptowano

2017-12-07

online

2018-01-10

Twórcy

autor

Andrea Seppi

• L-4364,

Identyfikatory

DOI

10.1515/coma-2017-0013