Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
MULTIPLE GENUS 2 HEEGAARD SPLITTINGS: A MISSED CASE
 

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 3-manifolds 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 3-manifold. 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 non-isotopic 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 3-manifold 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

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics