3-manifolds as viewed from the curve complex
| dc.creator | Hempel, John | |
| dc.date | 1997-12-03 | |
| dc.date.accessioned | 2026-07-07T05:23:21Z | |
| dc.date.available | 2026-07-07T05:23:21Z | |
| dc.description | 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. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/math/9712220 | |
| dc.identifier | http://arxiv.org/abs/math/9712220 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76403 | |
| dc.subject | Geometric Topology | |
| dc.title | 3-manifolds as viewed from the curve complex | |
| dc.type | text |