Angled decompositions of arborescent link complements

Details Angled decompositions of arborescent link complements Angled decompositions of arborescent link complements

2006-10-26

arxiv.org/abs/math/0610775v3

Proceedings of the London Mathematical Society 98 (2009), Issue 2, 325-364

Mathematics

Geometric Topology

42 pages, 23 figures. Slightly expanded exposition and references

Scientific paper

10.1112/plms/pdn033

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 The main application is a new proof of a classical, unpublished theorem of Bonahon and Siebenmann: that all arborescent links, except for three simple families of exceptions, have hyperbolic complements.

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