Multiple genus 2 Heegaard splittings: a missed case

Abstract

A gap in a paper of Rubinstein-Scharlemann 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 the original 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.

Reference to arxiv:1002.4887 added

References in corpus (2)

• A classification of pairs of disjoint nonparallel primitives in the boundary of a genus two handlebody
• A closed orientable 3-manifold with distinct distance three genus two Heegaard splittings

Cited by in corpus (7)

• Heegaard splittings of distance exactly $n$
• Non-uniqueness of high distance Heegaard splittings
• On keen Heegaard splittings
• A closed orientable 3-manifold with distinct distance three genus two Heegaard splittings
• A refinement of Johnson's bounding for the stable genera of Heegaard splittings
• On quotient orbifolds of hyperbolic 3-manifolds of genus two
• Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds