Comparing Heegaard and JSJ structures of orientable 3-manifolds

Martin Scharlemann; Jennifer Schultens

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arXiv · math/9802101

Comparing Heegaard and JSJ structures of orientable 3-manifolds

Martin Scharlemann·Jennifer Schultens

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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.

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BibTeX RIS

Martin Scharlemann, Jennifer Schultens. 1998-02-20. Comparing Heegaard and JSJ structures of orientable 3-manifolds. https://arxiv.org/abs/math/9802101

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