Character varieties in low-dimensional topology
报告题目(Title)：Character varieties in low-dimensional topology
报告人(Speaker)：陈海苗（北京工商大学）
地点(Place)：后主楼1220
时间(Time)：2019年11月22日15:00-16:00
邀请人(Inviter)：程志云
报告摘要
Suppose $Y$ is a discrete group and $G$ is a linear group. A homomorphism $Y\to G$ is called a {\it$G$-representation} of $Y$. An semi-simple $G$-representation $f$ is up to conjugacy uniquely determined by its {\it character}, which by definition is the function $Y\to\mathbb{C}$ sending $y$ to ${\rm tr}(f(y))$. All of these characters form the {\it $G$-character variety} of $Y$. If $Y$ is the fundamental group of a 3-manifold $M$, then the character variety encodes much information on $M$. In this talk the following about character varieties will be introduced: (1) basic notions and facts; (2) their roles in low-dimensional topology; (3) relations to quantum invariants; (4) proceedings of some research topics.
