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arXiv · 1908.05112

Geometric transition from hyperbolic to anti-de Sitter structures in dimension four

Stefano Riolo·Andrea Seppi
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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.

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Stefano Riolo, Andrea Seppi. 2019-08-14. Geometric transition from hyperbolic to anti-de Sitter structures in dimension four. https://doi.org/10.2422/2036-2145.202005_031

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