Geometry & Topology, Vol. 4 (2000) Paper no. 12, pages 369--395.

Taut ideal triangulations of 3-manifolds

Marc Lackenby

Abstract. 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.

Keywords. Taut, ideal triangulation, foliation, singular genus

AMS subject classification. Primary: 57N10. Secondary: 57M25.

DOI: 10.2140/gt.2000.4.369

E-print: arXiv:math.GT/0003132

Submitted to GT on 13 April 2000. (Revised 2 November 2000.) Paper accepted 10 October 2000. Paper published 4 November 2000.

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Marc Lackenby
Mathematical Institute, Oxford University, 24-29 St Giles'
Oxford OX1 3LB, UK
Email: lackenby@maths.ox.ac.uk

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