The Weber-Seifert dodecahedral space: Theory, algorithms and computation in 3-manifold topology
by Ben Burton
Abstract: The Weber-Seifert dodecahedral space is formed by identifying opposite
faces of a dodecahedron with a 3/10 twist, and was one of the first
known examples of a hyperbolic 3-manifold. Thurston conjectured in 1980
that this space was non-Haken, and recently this was proven to be true.
The proof involves a blend of theoretical, algorithmic and computational
techniques, and the aim of this talk is to piece together the different
techniques involved. This includes the theoretical methods of Haken and
Jaco/Oertel, the optimised enumeration algorithms of Tollefson, Letscher
and the speaker, new pruning techniques developed in conjunction with
Rubinstein and Tillmann, and the final computational results obtained
using the software package Regina.
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