Geometric transition from hyperbolic to anti-de Sitter structures in dimension four
Geometric Topology
2022-04-04 v3 Differential Geometry
Abstract
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 cuboctahedron. 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.
Keywords
Cite
@article{arxiv.1908.05112,
title = {Geometric transition from hyperbolic to anti-de Sitter structures in dimension four},
author = {Stefano Riolo and Andrea Seppi},
journal= {arXiv preprint arXiv:1908.05112},
year = {2022}
}
Comments
50 pages, 27 figures (many of the figures use colours). To appear in Annali della Scuola Normale Superiore, Classe di Scienze