The disjoint curve property
几何拓扑
2014-11-11 v1
摘要
A Heegaard splitting of a closed, orientable three-manifold satisfies the disjoint curve property if the splitting surface contains an essential simple closed curve and each handlebody contains an essential disk disjoint from this curve [Thompson, 1999]. A splitting is full if it does not have the disjoint curve property. This paper shows that in a closed, orientable three-manifold all splittings of sufficiently large genus have the disjoint curve property. From this and a solution to the generalized Waldhausen conjecture it would follow that any closed, orientable three manifold contains only finitely many full splittings.
引用
@article{arxiv.math/0401399,
title = {The disjoint curve property},
author = {Saul Schleimer},
journal= {arXiv preprint arXiv:math/0401399},
year = {2014}
}
备注
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper3.abs.html