3-manifolds as viewed from the curve complex
摘要
A Heegaard diagram for a 3-manifold is regarded as a pair of simplexes in the complex of curves on a surface and a Heegaard splitting as a pair of subcomplexes generated by the equivalent diagrams. We relate geometric and combinatorial properties of these subcomplexes with topological properties of the manifold and/or the associated splitting. For example we show that for any splitting of a 3-manifold which is Seifert fibered or which contains an essential torus the subcomplexes are at a distance at most two apart in the simplicial distance on the curve complex; whereas there are splittings in which the subcomplexes are arbitrarily far apart. We also give obstructions, computable from a given diagram, to being Seifert fibered or to containing an essential torus.
引用
@article{arxiv.math/9712220,
title = {3-manifolds as viewed from the curve complex},
author = {John Hempel},
journal= {arXiv preprint arXiv:math/9712220},
year = {2007}
}
备注
29 pages