Geometry & Topology Monographs 2 (1999), Proceedings of the Kirbyfest, paper no. 24, pages 489-553.

Genus two Heegaard splittings of orientable three-manifolds

Hyam Rubinstein, Martin Scharlemann

Abstract. It was shown by Bonahon-Otal and Hodgson-Rubinstein that any two genus-one Heegaard splittings of the same 3-manifold (typically a lens space) are isotopic. On the other hand, it was shown by Boileau, Collins and Zieschang that certain Seifert manifolds have distinct genus-two Heegaard splittings. In an earlier paper, we presented a technique for comparing Heegaard splittings of the same manifold and, using this technique, derived the uniqueness theorem for lens space splittings as a simple corollary. Here we use a similar technique to examine, in general, ways in which two non-isotopic genus-two Heegard splittings of the same 3-manifold compare, with a particular focus on how the corresponding hyperelliptic involutions are related.

Keywords. Heegaard splitting, Seifert manifold, hyperelliptic involution

AMS subject classification. Primary: 57N10. Secondary: 57M50.

E-print: arXiv:math.GT/9712262

Submitted: 10 September 1998. (Revised: 8 June 1999.) Published: 22 November 1999.

Notes on file formats

Hyam Rubinstein, Martin Scharlemann

Department of Mathematics, University of Melbourne
Parkville, Vic 3052, Australia

Mathematics Department, University of California
Santa Barbara, CA 93106, USA


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