On amalgamations of Heegaard splittings with high distance

DOI10.1090/S0002-9939-08-09642-1zbMath1162.57013MaRDI QIDQ3605028

Guo-Qiu Yang, Feng Chun Lei

Publication date: 25 February 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Heegaard splittingamalgamationHeegaard distance

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50)

Related Items (18)

A note on the planar surface sum of Heegaard splittings ⋮ A necessary and sufficient condition for a surface sum of two handlebodies to be a handlebody ⋮ A note on bicompressible surface and unstabilized amalgamated Heegaard splitting ⋮ Distance degenerating handle additions ⋮ Bilateral self-amalgamation of a Heegaard splitting and Hempel distance ⋮ Equivariant Heegaard genus of reducible 3-manifolds ⋮ Minimal Heegaard genus of amalgamated 3-manifolds ⋮ A sufficient condition for the genus of an amalgamated 3-manifold not to go down ⋮ On unstabilized Heegaard splittings of amalgamated 3-manifolds ⋮ Local uniqueness of certain geodesics related to Heegaard splittings ⋮ The amalgamation of high distance Heegaard splittings along tori ⋮ On weakly keen Heegaard splittings with distance 2 ⋮ The self-amalgamation of high distance Heegaard splittings is always efficient ⋮ Heegaard genera of high distance are additive under annulus sum ⋮ A note on Heegaard splittings of amalgamated 3-manifolds ⋮ Amalgamations of Heegaard splittings in 3-manifolds without some essential surfaces ⋮ Some results on Heegaard splitting ⋮ A necessary and sufficient condition for a Heegaard splitting to be keen weakly reducible

Cites Work

• Heegaard splittings of Haken manifolds have bounded distance.
• The amalgamation of high distance Heegaard splittings is always efficient
• Reducing Heegaard splittings
• Local detection of strongly irreducible Heegaard splittings
• Additivity of tunnel number for small knots
• The Heegaard genus of amalgamated 3-manifolds
• Sweepouts of amalgamated 3-manifolds
• Alternate Heegaard genus bounds distance
• Separating incompressible surfaces and stabilizations of Heegaard splittings
• The Classification of Heegaard Splittings for (Compact Orient Able Surface) × S¹
• 3-manifolds as viewed from the curve complex
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