#### Volume 12, issue 1 (2008)

 Recent Issues
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Characteristic subsurfaces, character varieties and Dehn fillings

### Steve Boyer, Marc Culler, Peter B Shalen and Xingru Zhang

Geometry & Topology 12 (2008) 233–297
##### Abstract

Let $M$ be a one-cusped hyperbolic $3$–manifold. A slope on the boundary of the compact core of $M$ is called exceptional if the corresponding Dehn filling produces a non-hyperbolic manifold. We give new upper bounds for the distance between two exceptional slopes $\alpha$ and $\beta$ in several situations. These include cases where $M\left(\beta \right)$ is reducible and where $M\left(\alpha \right)$ has finite ${\pi }_{1}$, or $M\left(\alpha \right)$ is very small, or $M\left(\alpha \right)$ admits a ${\pi }_{1}$–injective immersed torus.

##### Keywords
characteristic subsurfaces, character varieties, Dehn filling
##### Mathematical Subject Classification 2000
Primary: 57M25, 57M50, 57M99