### 3-manifolds and lagrangian subspaces of character varieties

- Series
- Geometry Topology Seminar
- Time
- Monday, October 6, 2008 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 269
- Speaker
- A. Sikora – SUNY Buffalo

W. Goldman proved that the SL(2)-character variety X(F) of a closed surface F is a holonomic symplectic manifold. He also showed that the Sl(2)-characters of every 3-manifold with boundary F form an isotropic subspace of X(F). In fact, for all 3-manifolds whose SL(2)-representations are easy to analyze, these representations form a Lagrangian space. In this talk, we are going to construct explicit examples of 3-manifolds M bounding surfaces of arbitrary genus, whose spaces of SL(2)-characters have dimension as small as possible. We discuss relevance of this problem to quantum and classical low-dimensional topology.