Geometry and Topology Seminar
The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Shaosai Huang.
|Sept. 14||Teddy Einstein (UIC)||Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes||(Dymarz)|
|Oct. 12||Marissa Loving||TBA||(Kent)|
|Oct. 19||Sara Maloni||TBA||(Kent)|
|Nov. 16||Xiangdong Xie||TBA||(Dymarz)|
"Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes"
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.
Archive of past Geometry seminars