Distressing Math Collective with Ziwei Tan
Join the Distressing Math Collective for a talk on "Hyperbolic Handle-body in Compact and Orientable Three-manifolds" with Ziwei Tan '25! Snacks will be served starting at 6:30 p.m. in the Math Lounge!
Abstract:
Given any compact orientable 3-manifold, we can cap off its spherical boundaries with balls and remove any torus boundaries. The resulting manifold contains a knot with a hyperbolic complement, as demonstrated by Robert Myers.
In this talk, we will extend this result to show that such a manifold contains a handlebody of any genus (at least 2) such that the complement is hyperbolic with totally geodesic boundary.
Furthermore, for any finite sequence of integers (a1,a2,…,an)(a_1, a_2, \ldots, a_n)(a1​,a2​,…,an​), every compact orientable 3-manifold contains a1a_1a1​ solid tori, a2a_2a2​ handlebodies of genus 2, …, and ana_nan​ handlebodies of genus nnn, all disjoint, such that the closure of the complement of their union is hyperbolic with totally geodesic boundary.
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