Regenerating hyperbolic cone 3-manifolds from dimension 2

Porti, Joan

Annales de l'Institut Fourier, Tome 63 (2013) no. 5, pp. 1971-2015.

On prouve qu’une 3-orbifold close qui fibre sur une 2-orbifold hyperbolique et polygonale admet une famille de structures coniques hyperboliques qu’on voit comme une régénérescence du polygone, pourvu que son périmètre soit minimal.

We prove that a closed 3-orbifold that fibers over a hyperbolic polygonal 2-orbifold admits a family of hyperbolic cone structures that are viewed as regenerations of the polygon, provided that the perimeter is minimal.

Classification : 57M50, 57N10
Keywords: orbifold, hyperbolic cone 3-manifold, degeneration, hyperbolic polygon, perimeter
Mot clés : orbifold, 3-variété conique hyperbolique, dégénérescense, polygone hyperbolique, périmètre

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