Title:
SL(2,C) character varieties in low-dimensional topology:
Connections with number theory and algebraic geometry.
Lecturer: Alan Reid, Rice University
Abstract:
Let G be a finitely generated group. In these lecture we will
study the collection R(G) of homomorphisms G---> SL(2,C). This has the
structure of an algebraic set. We will also study the associated character
variety which arises a certain quotient X(G) of R(G) (essentially by the
conjugation action). We will mainly be interested in groups that arise in
low-dimensional topology and geometry; e.g. free groups, surface groups
and knot groups. There will be many examples and explicit computations.
We will discuss these in the context of number theoretic and algebraic
questions about components in the character variety.