Flipping and stabilizing Heegaard splittings

Abstract

We show that the number of stabilizations needed to interchange the handlebodies of a Heegaard splitting of a closed 3-manifold by an isotopy is bounded below by the smaller of twice its genus or half its Hempel distance. This is a combinatorial version of a proof by Hass, Thompson and Thurston of a similar theorem, but with an explicit bound in terms of distance. We also show that in a 3-manifold with boundary, the stable genus of a Heegaard splitting and a boundary stabilization of itself is bounded below by the same value.

22 pages, 7 figures

References in corpus (1)

• Stable functions and common stabilizations of Heegaard splittings

Cited by in corpus (11)

• Bounding the stable genera of Heegaard splittings from below
• Flipping bridge surfaces and bounds on the stable bridge number
• Heegaard splittings of sufficiently complicated 3-manifolds I: Stabilization
• Heegaard splittings with large subsurface distances
• Stabilizations of Heegaard splittings of sufficiently complicated 3-manifolds (Preliminary Report)
• A refinement of Johnson's bounding for the stable genera of Heegaard splittings
• Stabilizing Heegaard Splittings of High-Distance Knots
• An estimation of Hempel distance by using Reeb graph
• Stabilization, amalgamation, and curves of intersection of Heegaard splittings
• Mapping class groups of medium distance Heegaard splittings
• On the union stabilization of two Heegaard splittings