Taut ideal triangulations of 3–manifolds

Lackenby, Marc¹

¹ Mathematical Institute, Oxford University, 24–29 St Giles’, Oxford OX1 3LB, United Kingdom

Geometry & topology, Tome 4 (2000) no. 1, pp. 369-395.

Résumé

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.

Détail

DOI : 10.2140/gt.2000.4.369

Keywords: taut, ideal triangulation, foliation, singular genus

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