Geometry & Topology

Characteristic subsurfaces, character varieties and Dehn fillings

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

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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

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M50: Geometric structures on low-dimensional manifolds 57M99: None of the above, but in this section

Keywords
characteristic subsurfaces character varieties Dehn filling

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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