CRITICAL HEEGAARD SURFACES OBTAINED BY SELF-AMALGAMATION

DOI10.1142/S0218216513500156zbMath1270.57056arXiv1301.5372MaRDI QIDQ5300093

Qiang E, Feng Chun Lei

Publication date: 24 June 2013

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

Full work available at URL: https://arxiv.org/abs/1301.5372

zbMATH Keywords

surface bundleHeegaard distanceself-amalgamationcritical Heegaard surface

Mathematics Subject Classification ID

General low-dimensional topology (57M99)

Related Items (11)

Unstabilized and uncritical dual Heegaard splitting of product \(I\)-bundle ⋮ A note on bicompressible surface and unstabilized amalgamated Heegaard splitting ⋮ On keen weakly reducible Heegaard splittings ⋮ Minimal partitions for critical Heegaard splittings ⋮ On unstabilized Heegaard splittings of amalgamated 3-manifolds ⋮ On unstabilized genus three critical Heegaard surfaces ⋮ Unnamed Item ⋮ Topologically minimal surfaces versus self-amalgamated Heegaard surfaces ⋮ A topologically minimal canonical Heegaard splitting of a surface bundle is critical ⋮ Unstabilized and uncritical self-amalgamation along essential subsurfaces ⋮ On topologically minimal surfaces of high genus

Cites Work

• Surface bundles versus Heegaard splittings
• Connected sums of unstabilized Heegaard splittings are unstabilized
• Topological index theory for surfaces in 3-manifolds
• Reducing Heegaard splittings
• Heegaard splittings of \((\text{surface})\times I\) are standard
• Critical Heegaard surfaces obtained by amalgamation
• Unstabilized self-amalgamation of a Heegaard splitting
• On the existence of high index topologically minimal surfaces
• Critical Heegaard surfaces
• 3-manifolds as viewed from the curve complex

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