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

DOI:
https://doi.org/10.1090/S0002-9947-00-02654-4

Published electronically:
September 15, 2000

MathSciNet review:
1804508

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Abstract | References | Similar Articles | Additional Information

Abstract: The Heegaard genus of an irreducible closed orientable -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 of the complementary components are not Seifert fibered, then . This generalizes work of Kobayashi. The Heegaard genus also puts explicit bounds on the complexity of the Seifert pieces. For example, if the union of the Seifert pieces has base space and exceptional fibers, then .

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Additional Information

**Martin Scharlemann**

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

Email:
mgscharl@math.ucsb.edu

**Jennifer Schultens**

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

Email:
jcs@mathcs.emory.edu

DOI:
https://doi.org/10.1090/S0002-9947-00-02654-4

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