## Topology & Geometric Group Theory Seminar

## Fall 2009

### 1:30 – 2:30, Malott 203

Tuesday, November 3

**Adam
Sikora**, University at Buffalo

*Character varieties*

Given a topological space Y, the space of representations of
π_{1}(Y) into an algebraic group G, considered up to
conjugation, is called the G-character variety of Y and it is denoted
by X_{G}(Y). If F is a closed surface, then X_{G}(F)
has a symplectic structure. Let M be a 3-dimensional manifold with
boundary F. In this talk we will discuss the question whether the
image of X_{G}(M) in X_{G}(F) is a Lagrangian
submanifold. There is a significant amount of confusion concerning
this issue in the literature. Along the way, we will survey some
fundamental properties of character varieties.

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