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.Comment: Published in Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper12.abs.htm