Heegaard splittings with (disk, essential surface) pairs that intersect in one point

Author:
Jung Hoon Lee

Journal:
Proc. Amer. Math. Soc. **138** (2010), 1877-1888

MSC (2000):
Primary 57M50, 57M25

DOI:
https://doi.org/10.1090/S0002-9939-09-10147-8

Published electronically:
December 18, 2009

MathSciNet review:
2587472

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a Heegaard splitting of a -manifold having an essential disk in and an essential surface in with .

From , we obtain another Heegaard splitting by removing a neighborhood of from and attaching it to . As an application, by using a theorem due to Casson and Gordon,

we give examples of -manifolds admitting two Heegaard splittings of distinct genera, where one of them is a strongly irreducible non-minimal genus splitting and it is obtained from the other by the above construction.

We also show that all Heegaard splittings of a Seifert fibered space are related via the above construction.

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Additional Information

**Jung Hoon Lee**

Affiliation:
School of Mathematics, Korea Institute for Advanced Study, 207-43, Cheongnyangni 2-dong, Dongdaemun-gu, Seoul, Korea

Email:
jhlee@kias.re.kr

DOI:
https://doi.org/10.1090/S0002-9939-09-10147-8

Keywords:
Heegaard splitting,
essential surface,
Seifert fibered space,
strongly irreducible

Received by editor(s):
January 4, 2009

Received by editor(s) in revised form:
May 25, 2009, and August 4, 2009

Published electronically:
December 18, 2009

Communicated by:
Daniel Ruberman

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.