Thurston’s bounded image theorem

Lecuire, Cyril¹ ; Ohshika, Ken’ichi²

¹ Laboratoire Emile Picard, Université Paul Sabatier, Toulouse, France, ENS de Lyon site Monod, UMPA UMR 5669 CNRS, Lyon, France
² Department of Mathematics, Faculty of Science, Gakushuin University, Tokyo, Japan

Geometry & topology, Tome 28 (2024) no. 6, pp. 2971-2999.

Résumé

Thurston’s bounded image theorem is one of the key steps in his proof of the uniformisation theorem for Haken manifolds. Thurston never published its proof, and no proof has previously been known, although a proof of its weaker version, called the bounded orbit theorem, is known. We give a proof of the original bounded image theorem, relying on recent development of Kleinian group theory.

Détail

DOI : 10.2140/gt.2024.28.2971

Keywords: hyperbolic $3$–manifold, Kleinian group, skinning map

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