English

Taut ideal triangulations of 3-manifolds

Geometric Topology 2014-11-11 v2

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

Cite

@article{arxiv.math/0003132,
  title  = {Taut ideal triangulations of 3-manifolds},
  author = {Marc Lackenby},
  journal= {arXiv preprint arXiv:math/0003132},
  year   = {2014}
}

Comments

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