Destabilizing amalgamated Heegaard splittings

Abstract

We construct a sequence of pairs of 3-manifolds each with torus boundary and with the following two properties: 1) For the result of a carefully chosen glueing of the nth pair of 3-manifolds along their boundary tori, the ratio of the genus of the resulting 3-manifold to the sum of the genera of the pair of 3-manifolds is less than 1/2. 2) The result of amalgamating certain unstabilized Heegaard splittings of the pair of 3-manifolds to form a Heegaard splitting of the resulting 3-manifold produces a stabilized Heegaard splitting that can be destabilized successively n times.

This is the version published by Geometry & Topology Monographs on 3 December 2007

References in corpus (3)

• Sweepouts of amalgamated 3-manifolds
• Stabilizations of Reducible Heegaard Splittings
• Heegaard genus formula for Haken manifolds

Cited by in corpus (7)

• Degeneration of Heegaard genus, a survey
• A characteristics for a surface sum of two handlebodies along an annulus or a once-punctured torus to be a handlebody
• Heegaard splittings of sufficiently complicated 3-manifolds II: Amalgamation
• Additivity of Heegaard genera of bounded surface sums
• Stabilization, amalgamation, and curves of intersection of Heegaard splittings
• On the width of complicated JSJ decompositions
• Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds