Multiple genus 2 Heegaard splittings: a missed case

Abstract

A gap in [H Rubinstein, M Scharlemann, Genus two Heegaard splittings of orientable 3–manifolds, in “Proceedings of the Kirbyfest”, Geom. Topol. Monogr. 2 (1999) 489–553] is explored: new examples are found of closed orientable 3–manifolds with possibly multiple genus 2 Heegaard splittings. Properties common to all the examples in that paper are not universally shared by the new examples: some of the new examples have Hempel distance 3, and it is not clear that a single stabilization always makes the multiple splittings isotopic.