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 π1(Y) into an algebraic group G, considered up to conjugation, is called the G-character variety of Y and it is denoted by XG(Y). If F is a closed surface, then XG(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 XG(M) in XG(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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