JournalslemVol. 57, No. 1/2pp. 23–56

From spaces of polygons to spaces of polyhedra following Bavard, Ghys and Thurston

  • François Fillastre

    Université de Cergy-Pontoise, France
From spaces of polygons to spaces of polyhedra following Bavard, Ghys and Thurston cover
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Abstract

Following work of W.P.~Thurston, C.~Bavard and É. Ghys constructed particular hyperbolic polyhedra from spaces of deformations of Euclidean polygons. We present this construction as a straightforward consequence of the theory of mixed-volumes. The gluing of these polyhedra can be isometrically embedded into complex hyperbolic cone-manifolds constructed by Thurston from spaces of deformations of Euclidean polyhedra. It is then possible to deduce the metric structure of the spaces of polygons embedded in complex hyperbolic orbifolds discovered by P. Deligne and G.D. Mostow.

Cite this article

François Fillastre, From spaces of polygons to spaces of polyhedra following Bavard, Ghys and Thurston. Enseign. Math. 57 (2011), no. 1, pp. 23–56

DOI 10.4171/LEM/57-1-2