Ideal tetrahedra and their duals in 3d geometry (Catherine Meusburger, Friedrich–Alexander University)

20.11.2018 15:30

Ideal hyperbolic tetrahedra play an important role in the construction of 3d hyperbolic manifolds. Their volume is given by the classical dilogarithm, which generates the mapping class group action on Teichmuller space. Recently, the notion of a hyperbolic tetrahedron was generalized to 3d anti de Sitter space and to half-pipe space, a 3d homogeneous space with a degenerate metric. We give a unified description of these generalized ideal tetrahedra and compute their volumes in terms of their dihedral angles. We show that the generalized ideal tetrahedra define dual tetrahedra in 3d Minkowski, de Sitter and anti de Sitter space and that their dihedral angles describe the edge lengths and Lorentzian angles of their duals. It turns out that the volume functions of the generalized ideal tetrahedra generate mapping class group actions on sectors of moduli spaces of flat connections that describe cusped globally hyperbolic 3d Lorentzian manifolds of constant curvature.

This is joint work in progress with Carlos Scarinci.

Lieu

Bâtiment: Villa Battelle

Séminaire "Groupes de Lie et espaces des modules"

entrée libre