No CrossRef data available.
Article contents
Parity criterion for unstabilized Heegaard splittings
Published online by Cambridge University Press: 16 March 2010
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
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 Unpublished.Google Scholar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