We will cover recent topics in hyperbolic 3-manifolds and knot
theory. This semester the plan is to go through the following papers:
-
An alternative approach to hyperbolic structures on link complements
Morwen Thistlethwaite and Anastasiia Tsvietkova,
Algebraic & Geometric Topology
Arxiv
Abstract: An alternative method is described for determining the hyperbolic structure on a link complement, and some of its consequences are examined. The method uses ideal polygons bounding the regions of a link diagram rather than ideal triangulation of the complement.
- Exact volume of hyperbolic 2-bridge links
Anastasiia Tsvietkova, Communications in Analysis and Geometry,
ArXiv
Abstract:
For hyperbolic 2-bridge links, we give formulae that allow one to find the exact volume, i.e. to construct a polynomial and to find volume as an analytic function of one of its roots. The computation is performed directly from a reduced, alternating link diagram.
All students are welcome. This seminar is organized
by
Abhijit Champanerkar .