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 its genus.

Keywords

taut, ideal triangulation, foliation, singular genus

Mathematical Subject Classification 2000

Primary: 57N10

Secondary: 57M25

References

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Publication

Received: 13 April 2000

Revised: 2 November 2000

Accepted: 10 October 2000

Published: 4 November 2000

Proposed: Robion Kirby

Seconded: Walter Neumann, David Gabai

Authors

Marc Lackenby
Mathematical Institute Oxford University 24–29 St Giles’ Oxford OX1 3LB United Kingdom

Volume 4, issue 1 (2000)

Marc Lackenby