The self-amalgamation of high distance Heegaard splittings is always efficient

DOI10.1016/j.topol.2010.01.013zbMath1189.57004OpenAlexW1965630094MaRDI QIDQ968906

Ruifeng Qiu, Kun Du

Publication date: 10 May 2010

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2010.01.013

zbMATH Keywords

stabilizationdistancestrongly irreducible

Mathematics Subject Classification ID

Related Items (15)

A note on the planar surface sum of Heegaard splittings ⋮ A note on the uniqueness of unstabilized Heegaard splittings of amalgamated 3-manifolds ⋮ A note on bicompressible surface and unstabilized amalgamated Heegaard splitting ⋮ Structure of Heegaard splitting of self-amalgamated 3-manifold ⋮ Bilateral self-amalgamation of a Heegaard splitting and Hempel distance ⋮ Minimal Heegaard genus of amalgamated 3-manifolds ⋮ On unstabilized Heegaard splittings of amalgamated 3-manifolds ⋮ A sufficient condition for a self-amalgamation of a Heegaard splitting to be unstabilized ⋮ A formula on Heegaard genus of self-amalgamated 3-manifolds ⋮ On weakly keen Heegaard splittings with distance 2 ⋮ A note on Heegaard genus of self-amalgamated 3-manifold ⋮ Unstabilized and uncritical self-amalgamation along essential subsurfaces ⋮ A note on Heegaard splittings of amalgamated 3-manifolds ⋮ Strongly irreducible self-amalgamation of a handlebody ⋮ A necessary and sufficient condition for a Heegaard splitting to be keen weakly reducible

Cites Work

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• Local detection of strongly irreducible Heegaard splittings
• Heegaard splittings of \((\text{surface})\times I\) are standard
• Saddle tangencies and the distance of Heegaard splittings
• Alternate Heegaard genus bounds distance
• Separating incompressible surfaces and stabilizations of Heegaard splittings
• On amalgamations of Heegaard splittings with high distance
• The Classification of Heegaard Splittings for (Compact Orient Able Surface) × S¹
• 3-manifolds as viewed from the curve complex

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