Geometric transition from hyperbolic to Anti-de Sitter structures in dimension four
Résumé
We provide the first examples of geometric transition from hyperbolic to Anti-de Sitter structures in dimension four, in a fashion similar to Danciger's three-dimensional examples. The main ingredient is a deformation of hyperbolic 4-polytopes, discovered by Kerckhoff and Storm, eventually collapsing to a 3-dimensional ideal cuboc-tahedron. We show the existence of a similar family of collapsing Anti-de Sitter polytopes, and join the two deformations by means of an opportune half-pipe orbifold structure. The desired examples of geometric transition are then obtained by gluing copies of the polytope.
Domaines
Topologie géométrique [math.GT]Origine | Fichiers produits par l'(les) auteur(s) |
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