It was shown by Bonahon-Otal and Hodgson-Rubinstein that any two genus-oneHeegaard splittings of the same 3-manifold (typically a lens space) areisotopic. On the other hand, it was shown by Boileau, Collins and Zieschangthat certain Seifert manifolds have distinct genus-two Heegaard splittings. Inan earlier paper, we presented a technique for comparing Heegaard splittings ofthe same manifold and, using this technique, derived the uniqueness theorem forlens space splittings as a simple corollary. Here we use a similar technique toexamine, in general, ways in which two non-isotopic genus-two Heegardsplittings of the same 3-manifold compare, with a particular focus on how thecorresponding hyperelliptic involutions are related.
展开▼
