Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T13:14:52.231Z Has data issue: false hasContentIssue false
  • English
  • Français

Parity criterion for unstabilized Heegaard splittings

Published online by Cambridge University Press:  16 March 2010

JUNG HOON LEE
JUNG HOON LEE*
Affiliation:
School of Mathematics, KIAS, 207-43, Cheongnyangni 2-dong, Dongdaemun-gu, Seoul, Korea. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We give a parity condition of a Heegaard diagram implying that it is unstabilized. As applications, we show that Heegaard splittings of 2-fold branched coverings of n-component, n-bridge links in S3 are unstabilized, and we also construct unstabilized Heegaard splittings by Dehn twists on any given Heegaard splitting.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 1 , July 2010 , pp. 115 - 125
Copyright
Copyright © Cambridge Philosophical Society 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Casson, A. and Gordon, C. Manifolds with irreducible Heegaard splittings of arbitrary large genus. Unpublished.Google Scholar
[2]Howards, H. and Schultens, J.Thin position for knots and 3-manifolds. Topology Appl. 155 (2008), no. 13, 1371–1381.CrossRefGoogle Scholar
[3]Kobayashi, T.A construction of 3-manifolds whose homeomorphism classes of Heegaard splittings have polynomial growth. Osaka J. Math. 29 (1992), no. 4, 653–674.Google Scholar
[4]Kobayashi, T.Casson–Gordon's rectangle condition of Heegaard diagrams and incompressible tori in 3-manifolds. Osaka J. Math. 25 (1988), no. 3, 553–573.Google Scholar
[5]Kobayashi, T.Heegaard splittings of exteriors of two bridge knots. Geom. Topol. 5 (2001), 609–650.CrossRefGoogle Scholar
[6]Lee, J. H. Parity condition for irreducibility of Heegaard splittings. preprint, arXiv:0812.0225.Google Scholar
[7]Moriah, Y. and Schultens, J.Irreducible Heegaard splittings of Seifert fibered spaces are either vertical or horizontal. Topology 37 (1998), no. 5, 1089–1112.CrossRefGoogle Scholar
[8]Saito, T.Disjoint pairs of annuli and disks for Heegaard splittings. J. Korean Math. Soc. 42 (2005), no. 4, 773–793.CrossRefGoogle Scholar
[9]Sedgwick, E.The irreducibility of Heegaard splittings of Seifert fibered spaces. Pacific J. Math. 190 (1999), no. 1, 173–199.CrossRefGoogle Scholar
[10]Schultens, J.The classfication of Heegaard splittings for (compact orientable surface) × S 1. Proc. London Math. Soc. (3) 67 (1993), no. 2, 425–448.CrossRefGoogle Scholar