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Comparing Heegaard and JSJ structures of orientable 3-manifolds

Authors: Martin Scharlemann and Jennifer Schultens
Journal: Trans. Amer. Math. Soc. 353 (2001), 557-584
MSC (2000): Primary 57M50
Published electronically: September 15, 2000
MathSciNet review: 1804508
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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 $p \leq g-1$. This 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 Seifert pieces has base space $P$ and $f$ exceptional fibers, then $f - \chi(P) \leq 3g - 3 - p$.

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Additional Information

Martin Scharlemann
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106

Jennifer Schultens
Affiliation: Department of Mathematics, Emory University, Atlanta, Georgia 30322

Received by editor(s): March 22, 1999
Published electronically: September 15, 2000
Additional Notes: Research supported in part by NSF grants and MSRI
Article copyright: © Copyright 2000 American Mathematical Society

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