The canonical decomposition of once-punctured torus bundles
By Marc Lackenby. 2001
47 citations recorded by the source corpus.
Abstract. 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/339767d359bd17d8f81aa3916089c2c9fda385a2
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In Geometry and Topology
- David Futer
- François Guéritaud
- Young-Eun Choi
- Francesco Costantino
- Jessica S. Purcell
- Bruno Martelli
In Mathematical Physics
- François Guéritaud
- David Futer
- Young-Eun Choi
- Francesco Costantino
- Jessica S. Purcell
- Bruno Martelli
Citations in the corpus
- On Canonical Triangulations of Once-Punctured Torus Bundles and Two-bridge link complements (2004, background): “Geometry & Topology 10 (2006) 1239–1284 1239 arXiv version: fonts, pagination and layout may vary from GT published version”
- Positively oriented ideal triangulations on hyperbolic three-manifolds (2004, background): “Recent work of Lackenby [7] shows that these triangulations are positively oriented at their respective complete structures.”