Geometry & Topology, Vol. 4 (2000)
Paper no. 12, pages 369--395.
Taut ideal triangulations of 3-manifolds
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
Taut, ideal triangulation, foliation, singular genus
AMS subject classification.
Submitted to GT on 13 April 2000.
(Revised 2 November 2000.)
Paper accepted 10 October 2000.
Paper published 4 November 2000.
Notes on file formats
Mathematical Institute, Oxford University, 24-29 St Giles'
Oxford OX1 3LB, UK
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