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.
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
[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)
[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)
[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
[Mo] Moriah, Y.: Heegaard Splittings and Group Presentations. Thesis, University of Texas, Austin 1986
[Se] Seifert, H.: Topologie dreidimensionaler gefaserte Räume. Acta Math.60, 147–238 (1933) (Translation by W. Heil, memo notes. Florida State University 1976
[Wa] Washington, L.C.: Introduction to Cyclotomic Fields. Graduate Texts in Math. Berlin Heidelberg New York: Springer 1983
[Wd1] Waldhausen, F.: Eine Klasse von 3 dimensionalen Mannigfaltigkeiten. I: Ivent. Math.3, 308–333 (1967); II: Invent. Math.3, 487–517 (1967)
[Wd2] Waldhausen, F.: Heegaard-Zerlegungen der 3-Sphäre. Topology7, 195–203 (1968)
[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)
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1007/BF01388781