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.
ÀÏÍõÂÛ̳ welcomes the full participation of all individuals in all aspects of campus life. Should you wish to request a disability-related accommodation for this event, please contact the event sponsor/coordinator. Requests should be made as early as possible.