Some results on Heegaard splitting

DOI10.1007/s10473-022-0612-zOpenAlexW4293561673MaRDI QIDQ2080984

Yanqing Zou, Ruifeng Qiu

Publication date: 12 October 2022

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10473-022-0612-z

zbMATH Keywords

stabilizationHeegaard distanceHeegaard genus

Mathematics Subject Classification ID

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

Cites Work

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• Infinitely many hyperbolic 3-manifolds admitting distance-\(d\) and genus-\(g\) Heegaard splittings
• The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).
• Heegaard splittings of Haken manifolds have bounded distance.
• A note on Heegaard splittings of amalgamated 3-manifolds
• An alternative proof that 3-manifolds can be triangulated
• A representation of orientable combinatorial 3-manifolds
• Finiteness of mapping class groups: locally large strongly irreducible Heegaard splittings
• Heegaard genus of closed orientable Seifert 3-manifolds
• Heegaard surfaces and measured laminations. I: the Waldhausen conjecture
• Casson-Gordon's rectangle condition of Heegaard diagrams and incompressible tori in 3-manifolds
• The amalgamation of high distance Heegaard splittings is always efficient
• Connected sums of unstabilized Heegaard splittings are unstabilized
• Knot exteriors with additive Heegaard genus and Morimoto's conjecture
• On the geometric and the algebraic rank of graph manifolds
• Heegaard surfaces and the distance of amalgamation
• Proximity in the curve complex: boundary reduction and bicompressible surfaces
• Stabilization of Heegaard splittings
• A proof of the Gordon conjecture
• Reducing Heegaard splittings
• Irreducible Heegaard splittings of Seifert fibered spaces are either vertical or horizontal
• The tunnel number of the sum of \(n\) knots is at least \(n\)
• Heegaard splittings of \((\text{surface})\times I\) are standard
• Thin position and Heegaard splittings of the 3-sphere
• An infinite collection of Heegaard splittings that are equivalent after one stabilization
• On the super additivity of tunnel number of knots
• Annuli in generalized Heegaard splittings and degeneration of tunnel number
• The Rubinstein-Scharlemann graphic of a 3-manifold as the discriminant set of a stable map
• Additivity of tunnel number for small knots
• Geometry of the complex of curves. II: Hierarchical structure
• On the classification of Heegaard splittings
• Non degenerating Dehn fillings on genus two Heegaard splittings of knots' complements
• Geometry of the complex of curves. I: Hyperbolicity
• On the Heegaard splitting of the torus \(T^ 3\)
• Zur dreidimensionalen Topologie
• Topology and combinatorics of 3-manifolds
• Comparing Heegaard splittings of non-Haken 3-manifolds
• Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds
• The lens space realization problem
• \(3\)-manifolds admitting locally large distance \(2\) Heegaard splittings
• The Heegaard distances cover all nonnegative integers
• Big Heegaard distance implies finite mapping class group
• The Heegaard genus of amalgamated 3-manifolds
• Heegaard splittings of distance exactly \(n\)
• Knot Floer homology detects fibred knots
• Saddle tangencies and the distance of Heegaard splittings
• High distance knots
• Alternate Heegaard genus bounds distance
• On irreducible 3-manifolds which are sufficiently large
• Heegaard-Zerlegungen der 3-Sphäre
• The stabilization problem for Heegaard splittings of Seifert fibered spaces
• A lower bound on tunnel number degeneration
• Affine structures in 3-manifolds. V: The triangulation theorem and Hauptvermutung
• Heegaard splittings and pseudo-Anosov maps
• On the degeneration of tunnel numbers under a connected sum
• Mapping class groups of medium distance Heegaard splittings
• Scindements de Heegaard des Variétés de Seifert Elliptiques et Euclidiennes
• Separating incompressible surfaces and stabilizations of Heegaard splittings
• Heegaard surfaces in Haken 3-manifolds
• Scindements de Heegaard des espaces lenticulaires
• On amalgamations of Heegaard splittings with high distance
• Stable functions and common stabilizations of Heegaard splittings
• Modifications and Cobounding Manifolds
• A Unique Decomposition Theorem for 3-Manifolds
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• The Classification of Heegaard Splittings for (Compact Orient Able Surface) × S¹
• Links with Unlinking Number One are Prime
• A CONSTRUCTION OF ARBITRARILY HIGH DEGENERATION OF TUNNEL NUMBERS OF KNOTS UNDER CONNECTED SUM
• Comparing Heegaard splittings -the bounded case
• On stability of Heegaard splittings
• The mapping class groups of reducible Heegaard splittings of genus two
• Every Two-Generator Knot is Prime
• Three-Dimensional Manifolds and Their Heegaard Diagrams
• There are Knots whose Tunnel Numbers go down under Connected Sum
• Rank and genus of 3-manifolds
• Bounding the stable genera of Heegaard splittings from below
• Heegaard surfaces and measured laminations, II: Non-Haken 3–manifolds
• Dehn surgery on knots
• 3-manifolds as viewed from the curve complex

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