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Proceedings of the London Mathematical Society Advance Access originally published online on July 18, 2008
Proceedings of the London Mathematical Society 2009 98(2):325-364; doi:10.1112/plms/pdn033
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© 2008 London Mathematical Society

Angled decompositions of arborescent link complements

David Futer

Mathematics Department
Temple University
Philadelphia, PA 19122
USA

François Guéritaud

Laboratoire de mathématiques
Université de Paris–Sud
91405 Orsay cedex
France
Francois.Gueritaud@normalesup.org

Received 18 December 2006. Revision received 24 January 2008.

This paper describes a way to subdivide a 3-manifold into angled blocks, namely polyhedral pieces that need not be simply connected. When the individual blocks carry dihedral angles that fit together in a consistent fashion, we prove that a manifold constructed from these blocks must be hyperbolic. The main application is a new proof of a classical, unpublished theorem of Bonahon and Siebenmann: that all arborescent links, except for three simple families of exceptions, have hyperbolic complements.

2000 Mathematics Subject Classification 57M25, 57M50.

Futer is partially supported by NSF grant DMS-0353717 (RTG), and Guéritaud is partially supported by NSF grant DMS-0103511.


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