Geometry & Topology

Taut ideal triangulations of 3–manifolds

Marc Lackenby

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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.

Article information

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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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

taut ideal triangulation foliation singular genus


Lackenby, Marc. Taut ideal triangulations of 3–manifolds. Geom. Topol. 4 (2000), no. 1, 369--395. doi:10.2140/gt.2000.4.369.

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