Surface bundles versus Heegaard splittings
几何拓扑
2007-05-23 v1
摘要
This paper studies Heegaard splittings of surface bundles via the curve complex of the fibre. The translation distance of the monodromy is the smallest distance it moves any vertex of the curve complex. We prove that the translation distance is bounded above in terms of the genus of any strongly irreducible Heegaard splitting. As a consequence, if a splitting surface has small genus compared to the translation distance of the monodromy, the splitting is standard.
引用
@article{arxiv.math/0212104,
title = {Surface bundles versus Heegaard splittings},
author = {David Bachman and Saul Schleimer},
journal= {arXiv preprint arXiv:math/0212104},
year = {2007}
}
备注
22 pages, 5 figures