HEEGAARD GENERA OF ANNULAR 3-MANIFOLDS

DOI10.1142/S0218216511009418zbMath1226.57030MaRDI QIDQ3004776

Ruifeng Qiu, Jiming Ma, Kun Du, Ming Xing Zhang

Publication date: 3 June 2011

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

zbMATH Keywords

primitivestrongly irreducibleHeegaard genera

Mathematics Subject Classification ID

Related Items (10)

A note on the uniqueness of unstabilized Heegaard splittings of amalgamated 3-manifolds ⋮ A note on bicompressible surface and unstabilized amalgamated Heegaard splitting ⋮ Minimal Heegaard genus of amalgamated 3-manifolds ⋮ On unstabilized Heegaard splittings of amalgamated 3-manifolds ⋮ Essential closed surfaces in surface sum of product \(I\)-bundle of closed surfaces ⋮ The amalgamation of high distance Heegaard splittings along tori ⋮ Heegaard genera of high distance are additive under annulus sum ⋮ The Heegaard genera of surface sums ⋮ A note on tunnel number of composite knots ⋮ A note on Heegaard splittings of amalgamated 3-manifolds

Cites Work

• Heegaard splittings of Haken manifolds have bounded distance.
• Heegaard genus of the connected sum of \(m\)-small knots
• The amalgamation of high distance Heegaard splittings is always efficient
• Proximity in the curve complex: boundary reduction and bicompressible surfaces
• Reducing Heegaard splittings
• The tunnel number of the sum of \(n\) knots is at least \(n\)
• Local detection of strongly irreducible Heegaard splittings
• Additivity of tunnel number for small knots
• Alternate Heegaard genus bounds distance
• Separating incompressible surfaces and stabilizations of Heegaard splittings
• 3-manifolds as viewed from the curve complex

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