September 23
Speaker: Katherine Goldman
Title: CAT(0) cube complexes, right-angled Artin groups, and the virtual fibering conjecture for 3-manifolds Part I: Ingredients of the proof
Abstract:
One of the great theorems in 3-manifold theory is the virtual fibering conjecture (now theorem), which states that every (closed, atoroidal, irreducible, infinite fundamental group) 3-manifold has a finite cover which is a fiber bundle over the circle, with fiber a surface. The geometrization theorem implies the theorem for non-hyperbolic 3-manifolds, while the proof of the conjecture for hyperbolic 3-manifolds utilizes many prominent objects of study in Geometric Group Theory, including special/CAT(0) cube complexes and right-angled Artin groups. In this talk we will describe these ingredients of the proof for hyperbolic 3-manifolds and explain how they are used in tandem with the virtual Haken conjecture (now theorem; another major result) to prove the full virtual fibering conjecture.
September 30
Speaker: Katherine Goldman
Title: CAT(0) cube complexes, right-angled Artin groups, and the virtual fibering conjecture for 3-manifolds Part II: Outline of the proof
Abstract:
After the general set up of last week, I will outline the proof with emphasis on the usage of CAT(0) cube complexes and right-angled Artin groups.
October 7
Speaker: Hyeran Cho
Title: Relative hyperbolicity and Dehn fillings
Abstract:
For a compact 3-manifold with torus boundary, we obtain a closed 3-manifold by attaching a solid torus to the boundary. This topological operation is called Dehn filling of spaces. From the group theoretic point of view, we consider a Dehn filling of a group where the group is the fundamental group of a complete finite volume hyperbolic manifold. Also, we can generalize this to relative hyperbolic groups and consider their Dehn fillings.
In this talk, I would like to introduce hyperbolic groups and relative hyperbolic groups. Moreover, we would consider Dehn fillings of relatively hyperbolic groups.
October 14
No meeting–fall break
October 24 (New day of the week!)
Speaker: James Marshall Reber
Title: The Weil-Petersson Metric
Abstract:
In this talk, we will present the definition of the Weil-Petersson metric on Teichmuller space and describe some interesting results related to the metric.