## Geometry & Topology

### Characteristic subsurfaces, character varieties and Dehn fillings

#### 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 $α$ and $β$ in several situations. These include cases where $M(β)$ is reducible and where $M(α)$ has finite $π1$, or $M(α)$ is very small, or $M(α)$ admits a $π1$–injective immersed torus.

#### Article information

Source
Geom. Topol., Volume 12, Number 1 (2008), 233-297.

Dates
Received: 23 November 2006
Accepted: 31 October 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800020

Digital Object Identifier
doi:10.2140/gt.2008.12.233

Mathematical Reviews number (MathSciNet)
MR2390346

Zentralblatt MATH identifier
1147.57002

#### Citation

Boyer, Steve; Culler, Marc; Shalen, Peter B; Zhang, Xingru. Characteristic subsurfaces, character varieties and Dehn fillings. Geom. Topol. 12 (2008), no. 1, 233--297. doi:10.2140/gt.2008.12.233. https://projecteuclid.org/euclid.gt/1513800020

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