Celebratio Mathematica

I. R. Aitchison and J. H. Rubinstein: “Fibered knots and involutions on homotopy spheres,” pp. 1–74 in Four-manifold theory (Durham, NH, 4–10 July 1982). Edited by C. Gordon and R. Kirby. Contemporary Mathematics 35. American Mathematical Society (Providence, RI), 1984. MR 780575 Zbl 0567.57015 incollection

Iain Roderick Aitchison	Related
Robion C. Kirby	Related	Volume
Cameron McAllan Gordon	Related	Volume

I. R. Aitchison and J. H. Rubinstein: “Combinatorial Dehn surgery on cubed and Haken 3-manifolds,” pp. 1–21 in Proceedings of the KirbyFest (Berkeley, CA, 22–26 June 1998). Edited by J. Hass and M. Scharlemann. Geometry & Topology Monographs 2. International Press (Cambridge, MA), 1999. Papers dedicated to Rob Kirby on the occasion of his 60th birthday. MR 1734399 Zbl 0948.57016 ArXiv 9911072 incollection

Robion C. Kirby	Related	Volume
Joel Hass	Related
Iain Roderick Aitchison	Related
Martin Scharlemann	Related	Volume

H. Rubinstein and M. Scharlemann: “Genus two Heegaard splittings of orientable three-manifolds,” pp. 489–553 in Proceedings of the KirbyFest (Berkeley, CA, 22–26 June 1998). Edited by J. Hass and M. Scharlemann. Geometry & Topology Monographs 2. International Press (Cambridge, MA), 1999. Papers dedicated to Rob Kirby on the occasion of his 60th birthday. MR 1734422 Zbl 0962.57013 ArXiv 9712262 incollection

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

Joel Hass	Related
Martin Scharlemann	Related	Volume
Robion C. Kirby	Related	Volume

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J. Hyam Rubinstein

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