Volume 4, issue 1 (2000)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Taut ideal triangulations of 3–manifolds

Marc Lackenby

Geometry & Topology 4 (2000) 369–395

arXiv: math.GT/0003132

Abstract

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
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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