Heegaard splittings with large subsurface distances

2010/02/16 by Jesse Johnson, Yair Minsky, Yoav Moriah · 1 citation
Mathematics · #math.GT #msc:57M

paper · pdf · doi:10.2140/agt.2010.10.2251

published as Algebr. Geom. Topol. 10 (2010) 2251-2275 · 23 pages and 5 figures

arxiv created 2010/02/16 · arxiv updated 2014/09/30

Abstract

We show that sub-surfaces of a Heegaard surface for which the relative Hempel distance of the splitting is sufficiently high have to appear in any Heegaard surface of genus bounded by half that distance.

Cited by

• Comparing h-genera, Bridge-1 genera and Heegaard genera of knots

Related

• One-sided and two-sided Heegaard splittings
• Non-uniqueness of high distance Heegaard splittings
• Surface bundles versus Heegaard splittings
• Decomposing Heegaard splittings along separating incompressible surfaces in 3-manifolds
• On keen Heegaard splittings