Angled decompositions of arborescent link complements

By David Futer, François Guéritaud. 2006

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 The main application is a new proof of a classical, unpublished theorem of Bonahon and Siebenmann: that all arborescent links, except for three simple families of exceptions, have hyperbolic complements.

Subfields: Civil and Structural Engineering, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1c9cddb2729b998ed99fa8d9de069489b3736b87