Skip to main content
Log in

Heegaard splittings of Seifert fibered spaces

  • Published:
Inventiones mathematicae Aims and scope

Summary

In this paper we give a classification theorem of genus two Heegaard splittings of Seifert fibered manifolds overS 2 with three exceptional fibers, except for when two of the exceptional fibers hava the same invariants with opposite orientation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • [Be] Beardon, A.F.: The Geometry of Discrete Groups. Graduate Texts in Mathematics, 91, Berlin, Heidelberg, New York: Springer 1983

    Google Scholar 

  • [B, C, Z] Boileau, M., Collins, D.J., Zieschang, H.: Scindements de Heegaard des petites variétés de Seifert. (Preprint)

  • [B, G, M] Birman, J.S., Gonzàles-Acuña, F., Montesionos, J.M.: Heegaard splittings of prime 3-manifolds are not unique. Mich. Math. J.23, 97–103 (1976)

    Google Scholar 

  • [B, O] Boileau, M., Otal, J.P.: Groupe des difféotopies de certains variétés de Seifert. C.R. Acad. Sci. Paris303, Serie 1. no 1 1986

  • [B, R, Z] Boileau, M., Rost, M., Zieschang, H.: On Heegaard Decompositions of Torus Exteriors and Related Seifert Fibered Spaces (to appear in Math. Ann.)

  • [Bo, O] Bonahon, F., Otal, J.P.: Scindements de Heegaard des espaces lenticulairés. Ann. Sci. Ec. Norm. Super.16, 451–466 (1983)

    Google Scholar 

  • [C, G] Casson, A.J., Gordon, C.: Manifolds with irreducible Heegaard splittings of arbitrarily high genus (to appear)

  • [L, S] Lyndon, C.L., Schupp, P.E.: Combinational Group Theory. Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  • [Mo] Moriah, Y.: Heegaard Splittings and Group Presentations. Thesis, University of Texas, Austin 1986

    Google Scholar 

  • [Se] Seifert, H.: Topologie dreidimensionaler gefaserte Räume. Acta Math.60, 147–238 (1933) (Translation by W. Heil, memo notes. Florida State University 1976

    Google Scholar 

  • [Wa] Washington, L.C.: Introduction to Cyclotomic Fields. Graduate Texts in Math. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  • [Wd1] Waldhausen, F.: Eine Klasse von 3 dimensionalen Mannigfaltigkeiten. I: Ivent. Math.3, 308–333 (1967); II: Invent. Math.3, 487–517 (1967)

    Google Scholar 

  • [Wd2] Waldhausen, F.: Heegaard-Zerlegungen der 3-Sphäre. Topology7, 195–203 (1968)

    Google Scholar 

  • [Wl] Wlodarski, L.: On the Equation cos α1+cos α2+cos α3+cos α4=0. Ann. Univ. Sci. Budapest. Eötvös. Sect. Math.12, 147–155 (1969)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moriah, Y. Heegaard splittings of Seifert fibered spaces. Invent Math 91, 465–481 (1988). https://doi.org/10.1007/BF01388781

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388781

Keywords

Navigation