## Using character varieties to find closed surfaces in 3-manifolds

Eric Chesebro (Montana)

Abstract

We will discuss the techniques developed by Culler and Shalen in the 80’s for using the $$SL(2,\mathbb{C})$$ character variety for a 3-manifold M to find essential surfaces in M. Most of the work in this area has focused on the case when the associated surfaces have nonempty boundary. Here we will introduce new results which apply when the associated surface is closed.