 
Summary: MULTIPLE GENUS 2 HEEGAARD SPLITTINGS: A
MISSED CASE
JOHN BERGE AND MARTIN SCHARLEMANN
Abstract. A gap in [RS] is filled: new examples are found of
closed orientable 3manifolds with possibly multiple genus 2 Hee
gaard splittings. Properties common to all the examples in [RS]
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.
1. Introduction
In 1998, Rubinstein and the second author [RS] studied the question
of when there could be more than one distinct genus 2 Heegaard split
ting of the same closed orientable 3manifold. The goal of the project
was modest: to provide a complete list of ways in which such multiple
splittings could be constructed, but with no claim that each example
on the list did in fact have multiple nonisotopic splittings (there could
be isotopies from one splitting to another that are not apparent). Nor
was there a claim that the list had no redundancies; a 3manifold and
its multiple splittings might appear more than once on the list. Such a
list would still be useful, for if every example on the list could be shown
