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Junior Topology
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Casandra Monroe, : A Talk Where Someone Defines Arithmetic Hyperbolic 3-Manifolds
Wednesday, March 31, 2021, 02:00pm - 03:00pm
The Figure-Eight Knot Complement, the Whitehead link complement, the complement of the Borromean rings, and the Magic manifold--what do they have in common? Well, they are nice 3-manifolds that we've given names to because they have had a lot of utility in the story of 3-manifold theory and the geometry of these objects. It turns out, part of what makes them so nice is that they are all arithmetic manifolds--but what does that mean? People have assured me that this property makes these manifolds very cool (some, like Thurston, write that they have a "special beauty"). Maybe this has happened to you too. In this talk, I hope to explain what they are, go over some examples, and talk about some cool results.

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