Heegaard surfaces and the distance of amalgamation

DOI10.2140/gt.2010.14.1871zbMath1207.57031arXiv0807.2869OpenAlexW3099519697MaRDI QIDQ991848

Tao Li

Publication date: 8 September 2010

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.2869

zbMATH Keywords

Heegaard splittingamalgamationcurve complex

Mathematics Subject Classification ID

Related Items (21)

A note on the planar surface sum of Heegaard splittings ⋮ A note on bicompressible surface and unstabilized amalgamated Heegaard splitting ⋮ Bilateral self-amalgamation of a Heegaard splitting and Hempel distance ⋮ Heegaard genus, degree‐one maps, and amalgamation of 3‐manifolds ⋮ Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds ⋮ Minimal Heegaard genus of amalgamated 3-manifolds ⋮ On unstabilized Heegaard splittings of amalgamated 3-manifolds ⋮ Computing Heegaard Genus is NP-Hard ⋮ On tunnel numbers of a cable knot and its companion ⋮ A sufficient condition for a self-amalgamation of a Heegaard splitting to be unstabilized ⋮ A formula on Heegaard genus of self-amalgamated 3-manifolds ⋮ Small 3-manifolds with large Heegaard distance ⋮ Rank and genus of 3-manifolds ⋮ The self-amalgamation of high distance Heegaard splittings is always efficient ⋮ A note on Heegaard genus of self-amalgamated 3-manifold ⋮ Unstabilized and uncritical self-amalgamation along essential subsurfaces ⋮ On the degeneration of tunnel numbers under a connected sum ⋮ Efficient triangulations and boundary slopes ⋮ Thin position and planar surfaces for graphs in the 3-sphere ⋮ Strongly irreducible self-amalgamation of a handlebody ⋮ Some results on Heegaard splitting

Cites Work

• Heegaard splittings of Haken manifolds have bounded distance.
• Heegaard surfaces and measured laminations. I: the Waldhausen conjecture
• Proximity in the curve complex: boundary reduction and bicompressible surfaces
• Reducing Heegaard splittings
• Local detection of strongly irreducible Heegaard splittings
• Heegaard splittings of \((\text{surface})\times I\) are standard
• Heegaard structures of negatively curved 3-manifolds
• Geometry of the complex of curves. I: Hyperbolicity
• Persistence of Heegaard structures under Dehn filling
• Immersed essential surfaces in hyperbolic 3-manifolds
• The Heegaard genus of amalgamated 3-manifolds
• Saddle tangencies and the distance of Heegaard splittings
• Sweepouts of amalgamated 3-manifolds
• Alternate Heegaard genus bounds distance
• Thin position and planar surfaces for graphs in the 3-sphere
• The Classification of Heegaard Splittings for (Compact Orient Able Surface) × S¹
• The Heegaard structure of Dehn filled manifolds
• 3-manifolds as viewed from the curve complex
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