Colloquium: Anastasiia Tsvietkova- University of California-Davis

Event Details

Title: Hyperbolic structures from links diagrams

As a result of Thurston’s Hyperbolization Theorem, many 3-manifolds have a hyperbolic metric or can be decomposed into pieces with hyperbolic metric. In particular, Thurston demonstrated that every link in S^3 is a torus link, a satellite link or a hyperbolic link and these three categories are mutually exclusive. Even though the geometric structure of a particular hyperbolic 3-manifold can be calculated, it is hard to relate it to (often more natural) topological and combinatorial descriptions of the manifold. We will discuss an alternative method for computing the hyperbolic structure of a hyperbolic link complement that allows to approach this task, and to make some observations about the intrinsic geometry just from a link diagram. The talk is based on joint work with M. Thistlethwaite, and on joint work with W. Neumann.