|Reflection groups in geometric group theory|
|Instructor：||Michael W. Davis [The Ohio State University]|
|Place：||Conference Room 1， Floor 1, Jin Chun Yuan West Building|
We will begin by discussing classical examples of groups generated by reflections on Euclidean space, the sphere or hyperbolic space. Next we will discuss the theory of Coxeter groups (or “abstract reflection groups”). Any Coxeter group can be realized as a reflection group on a certain contractible cell complex equipped with a polyhedral metric of nonpositive curvature. A version of this construction, called “the reflection group trick,” can be used to get new examples of aspherical manifolds.
Knowledge of basic topology and the geometry of metric spaces.
M.W. Davis, The Geometry and Topology of Coxeter Groups,