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EnglishWe 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.
| Titolo: | Geometric transition from hyperbolic to anti-de Sitter structures in dimension four | |
| Autore/i: | Riolo, Stefano; Seppi, Andrea | |
| Autore/i Unibo: | ||
| Anno: | 2022 | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.2422/2036-2145.202005_031 | |
| 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. | |
| Data stato definitivo: | 2022-03-31T20:41:39Z | |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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