Transition of convex core doubles from hyperbolic to Anti-de sitter geometry

Farid Diaf

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arXiv · 2307.14905

Transition of convex core doubles from hyperbolic to Anti-de sitter geometry

Farid Diaf

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Abstract

Let $\Sigma$ be a surface of negative Euler characteristic, homeomorphic to a closed surface, possibly with a finite number of points removed. In this paper, we present a construction method for a wide range of examples of geometric transition from hyperbolic to Anti-de Sitter structures via Half-pipe geometry on $\Sigma\times\mathbb{S}^1$, with cone singularities along a link. The main ingredient lies in studying the deformation of a convex core structure as the bending laminations of the upper and lower boundary components of the convex core uniformly collapse to zero.

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Farid Diaf. 2023-07-27. Transition of convex core doubles from hyperbolic to Anti-de sitter geometry. https://arxiv.org/abs/2307.14905

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