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Distressing Math Collective with Ziwei Tan

Oct 9
2024
7:00pm - 8:00pm
Hybrid (On Campus) Event - Park Science, Room 245

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.

Audience: BMC Community
Type(s): Student Activity/Club Event
Contact:
Leslie Cheng

ÐÓ°ÉÔ­°æÓ°Òô 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.