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Special Colloquium in Math: Dr. Hongbin Sun, UC Berkeley

"Arithmetic hyperbolic manifold groups contain nonseparable subgroups"

Monday, February 13, 2017
  3:40–5 p.m.


Location: Surge Building 284
  Parking Information

Category: Colloquium

Description: Given a group, whether all finitely generated subgroups are separable is an interesting group theoretical property, and it is closely related with low-dimensional topology, e.g. the virtual Haken conjecture (solved by Agol). I will show that, for almost all arithmetic hyperbolic manifolds with dimension at least 4, their fundamental groups contain nonseparable subgroups. The main ingredient is a study of certain graph of groups with hyperbolic 3-manifold groups as vertices, and the fact that hyperbolic 3-manifolds have a lot of virtual fibering structures. The proof also implies that, for a compact irreducible 3-manifold with empty or tori boundary, it supports one of eight Thurston's geometries if and only if its fundamental group is subgroup separable. 

Additional Information: Math Colloquiums

Open to: General Public
Admission: Free
Sponsor: Mathematics

Contact Information:
Dr. Yat Sun Poon

ypoon@ucr.edu