Taut ideal triangulations of 3-manifolds

Details Taut ideal triangulations of 3-manifolds Taut ideal triangulations of 3-manifolds

2000-03-22

arxiv.org/abs/math/0003132v2

Geom. Topol. 4(2000) 369-395

Mathematics

Geometric Topology

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

Scientific paper

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.

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