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Thurston's bounded image theorem

Cyril Lecuire and Ken’ichi Ohshika

Geometry & Topology 28 (2024) 2971–2999
Abstract

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.

Keywords
hyperbolic $3$–manifold, Kleinian group, skinning map
Mathematical Subject Classification
Primary: 30F40, 57K32
References
Publication
Received: 18 September 2022
Revised: 14 March 2023
Accepted: 22 April 2023
Published: 21 October 2024
Proposed: Ian Agol
Seconded: Mladen Bestvina, Dmitri Burago
Authors
Cyril Lecuire
Laboratoire Emile Picard
Université Paul Sabatier
Toulouse
France
ENS de Lyon site Monod
UMPA UMR 5669 CNRS
Lyon
France
Ken’ichi Ohshika
Department of Mathematics, Faculty of Science
Gakushuin University
Tokyo
Japan

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