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The canonical decomposition of once-punctured torus bundles

Abstract:
In this paper, we determine the canonical polyhedral decomposition of every hyperbolic once-punctured torus bundle over the circle. In fact, we show that the only ideal polyhedral decomposition that is straight in the hyperbolic structure and that is invariant under a certain involution is the ideal triangulation defined by Floyd and Hatcher. Unlike previous work on this problem, the techniques we use are not geometric. Instead, they involve angled polyhedral decompositions, thin position and a version of almost normal surface theory.
Publication status:
Published

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
COMMENTARII MATHEMATICI HELVETICI More from this journal
Volume:
78
Issue:
2
Pages:
363-384
Publication date:
2001-12-20
ISSN:
0010-2571
Language:
English
Keywords:
Pubs id:
pubs:17255
UUID:
uuid:8b01be04-54ca-40d3-88ee-fc770cbbcb2d
Local pid:
pubs:17255
Source identifiers:
17255
Deposit date:
2012-12-19

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