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Triangulations and verified computations for hyperbolic manifolds
Student-Run Geometry/Topology Seminar| Speaker: | Matthias Goerner, Pixar Animation Studios |
| Related Webpage: | http://www.unhyperbolic.org/ |
| Location: | 3106 MSB |
| Start time: | Tue, May 24 2016, 11:00AM |
Numerical algorithms cannot always be trusted. For example, (old versions of) SnapPy claim that "x101" and "x103" are two different hyperbolic manifolds even though Burton recognized that they are the same.
I will review the isomorphism signature, a complete invariant of the combinatorial type of a triangulation, and extend it through the canonical cell decomposition to the isometry signature which is a complete invariant of the isometry type of a cusped hyperbolic manifold. I will then talk about algorithms to verify rigorously the canonical cell decomposition and thus the isometry signature.
These invariants were essential for the creation of the census of Platonic manifolds.