Taut ideal triangulations of 3–manifolds
By Marc Lackenby. 2000
69 citations recorded by the source corpus.
A taut ideal triangulation of a 3{manifold is a topological ideal triangulation with extra combinatorial structure: a choice of transverse orientation on each ideal 2{simplex, satisfying two simple conditions. The aim of this paper is to demonstrate that taut ideal triangulations are very common, and that their behaviour is very similar to that of a taut foliation. For example, by studying normal surfaces in taut ideal triangulations, we give a new proof of Gabai’s result that the singular genus of a knot in the 3{sphere is equal to its genus.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9e4b1897f460dd89da36d53c05c2f05840a4a3f9
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
- W. Jaco
- J. Hyam Rubinstein
- Craig Hodgson
- Henry Segerman
- Stavros Garoufalidis
- Feng Luo
- Stephan Tillmann
- Thang T. Q. Lê
In Geometry and Topology
- W. Jaco
- J. Hyam Rubinstein
- Stavros Garoufalidis
- Craig Hodgson
- Henry Segerman
- Feng Luo
- David Glickenstein
- Tudor Dimofte
Citations in the corpus
- A combinatorial curvature flow for compact 3-manifolds with boundary (2004, background): “The work of Lackenby [ La2 ] gives some evidences that the following may have a positive answer.”
- 1-efficient triangulations and the index of a cusped hyperbolic 3-manifold (2013, methodology): “Remark 1.7 In Corollary 3.4, we note that a construction of Lackenby produces triangulations with taut angle structures, which are therefore 1–efficient, on all irreducible cusped 3–manifolds containing no essential annulus.”
- Layered-triangulations of 3-manifolds (2006, background): “There is an interesting connection between layered triangulations and foliations, following Lackenby’s view of how to construct taut ideal triangulations [19].”