Geometry & Topology
- Geom. Topol.
- Volume 4, Number 1 (2000), 369-395.
Taut ideal triangulations of 3–manifolds
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.
Geom. Topol., Volume 4, Number 1 (2000), 369-395.
Received: 13 April 2000
Revised: 2 November 2000
Accepted: 10 October 2000
First available in Project Euclid: 21 December 2017
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Lackenby, Marc. Taut ideal triangulations of 3–manifolds. Geom. Topol. 4 (2000), no. 1, 369--395. doi:10.2140/gt.2000.4.369. https://projecteuclid.org/euclid.gt/1513883289