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Characteristic subsurfaces, character varieties and Dehn fillings

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

Geometry and Topology 12 (2008) 233–297

DOI: 10.2140/gt.2008.12.233

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.

Keywords

characteristic subsurfaces, character varieties, Dehn filling

Mathematical Subject Classification

Primary: 57M25, 57M50, 57M99

References
Publication

Received: 23 November 2006
Accepted: 31 October 2007
Published: 12 March 2008
Proposed: Cameron Gordon
Seconded: Joan Birman, Martin Bridson

Authors
Steve Boyer
Département de mathématiques
Université du Québec à Montréal
PO Box 8888
Postal Station Centre-ville Montréal
Quebec H3C 3P8
Canada
http://www.cirget.uqam.ca/boyer/boyer.html
Marc Culler
Department of Mathematics, Statistics and Computer Science (M/C 249)
University of Illinois at Chicago
851 S Morgan St
Chicago, IL 60607-7045
http://www.math.uic.edu/~culler/
Peter B Shalen
Department of Mathematics, Statistics and Computer Science (M/C 249)
University of Illinois at Chicago
851 S Morgan St
Chicago IL 60607-7045
USA
http://www.math.uic.edu/~shalen/
Xingru Zhang
Department of Mathematics
SUNY at Buffalo
Buffalo NY 14260-2900
USA
http://www.math.buffalo.edu/~xinzhang/