Hyperbolic structures from link diagrams- Anastasiia Tsvietkova

Conference Title: GEAR Retreat 2012 Theme: Hyperbolic 3-manifolds (4 of 5) Title: Hyperbolic structures from link diagrams Speaker: Anastasiia Tsvietkova, University of Tennessee; Date and Time: Wednesday August 8, 14:40 Description: W. 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 W. Menasco that an alternating link represented by a prime diagram is either hyperbolic or a (2;n)-torus link. The talk will introduce an alternative method for computing the hyperbolic structure of the complement of a hyperbolic link. It allows computing the structure directly from the link diagram. Some of its consequences will be discussed, including a surprising rigidity property of certain tangles, and the formulas that allow one to calculate the exact hyperbolic volume, as well as complex volume, of hyperbolic 2-bridge links. This is joint work with M. Thistlethwaite. Sponsor: GEAR Network Local host: UIUC Department of Mathematics Funding provided by: National Science Foundation Research Networks in Mathematical Sciences programAbstract: Prof. Anastasia Tsvietkova, in this GEAR Retreat 2012 session on Hyperbolic 3-manifolds, will discuss an alternative method for computing the hyperbolic structure of the complement of a hyperbolic link.