Topology Seminar (Main Talk): Rigorous computations with an approximate Dirichlet domain

Seminar | January 23 | 5-6 p.m. | 3 Evans Hall

 Maria Trnkova, UC Davis

 Department of Mathematics

In this talk we address some problems concerning an approximate Dirichlet domain. We show that under some assumptions the approximate Dirichlet domain can work equally well as an exact Dirichlet domain. In particular, we consider a problem of tiling a hyperbolic ball with copies of the Dirichlet domain. This problem arises in the construction of the length spectrum algorithm which is for example implemented by the computer program SnapPea. Our result explains the empirical fact that the program works surprisingly well despite it does not use exact data. Also we demonstrate a rigorous verification if two words of a fundamental group of a hyperbolic 3-manifold are the same or not.