Comparing Heegaard and JSJ structures of orientable 3-manifolds
Geometric Topology
2007-05-23 v1
Abstract
The Heegaard genus g of an irreducible closed orientable 3-manifold puts a limit on the number and complexity of the pieces that arise in the Jaco-Shalen-Johannson decomposition of the manifold by its canonical tori. For example, if p of the complementary components are not Seifert fibered, then p < g. This result generalizes work of Kobayashi. The Heegaard genus g also puts explicit bounds on the complexity of the Seifert pieces. For example, if the union of the base spaces of the Seifert pieces has Euler characteristic X and there are a total of f exceptional fibers in the Seifert pieces, then f - X is no greater than 3g - 3 - p.
Keywords
Cite
@article{arxiv.math/9802101,
title = {Comparing Heegaard and JSJ structures of orientable 3-manifolds},
author = {Martin Scharlemann and Jennifer Schultens},
journal= {arXiv preprint arXiv:math/9802101},
year = {2007}
}
Comments
30 pages, 10 figures