On the topology of character varieties of once-punctured torus bundles

Contact: Gaetan Borot (gaetan.borot@hu-berlin.de)

https://hu-berlin.zoom.us/j/61686623112

Let M be a complete hyperbolic 3-manifold of finite volume. The seminal work of Thurston and Culler-Shalen established the SL(2,C)-character variety of the fundamental group of M as a powerful tool in the study of the topology of M. This talk focusses on the particular class of manifolds that are hyperbolic once-punctured torus bundles. These are generally very well understood. Yet, there are some interesting open questions regarding their character varieties, especially concerning their topology and how much topological information can be obtained from them about the bundles.

This talk gives a quick overview of Culler-Shalen theory, introduces the manifolds in the title, and explains some work with Youheng Yao (arXiv:2206.14954) concerning their character varieties.