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An alternative approach to hyperbolic structures on link complements
by
Anastasiia Tsvietkova
University of Tennessee, Knoxville
Coauthors: Morwen Thistlethwaite
Thurston demonstrated that every link in S3 is a torus link, a satellite link or a hyperbolic link and these three categories are mutually exclusive. It also follows from work of Menasco that an alternating link represented by a prime diagram is either hyperbolic or a (2, n)-torus link.
A new method for computing the hyperbolic structure of the complement of a hyperbolic link, based on ideal polygons bounding the regions of a diagram of the link rather than decomposition of the complement into ideal tetrahedra, was suggested by M. Thistlethwaite. Although the method is applicable to all diagrams of hyperbolic links under a few mild restrictions, it works particularly well for alternating (non-torus) links. The talk will introduce the basics of the method. Some applications will be discussed, including a surprising rigidity property of certain tangles, a new numerical invariant for tangles, and formulas that allow one to calculate the volume of 2-bridged links directly from the diagram.
Date received: November 5, 2011
Copyright © 2011 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbdt-15.