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Some results on Heegaard splitting (Q2080984)

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scientific article; zbMATH DE number 7600115

Language	Label	Description	Also known as
English	Some results on Heegaard splitting	scientific article; zbMATH DE number 7600115

Statements

scholarly article

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Some results on Heegaard splitting (English)

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Acta Mathematica Scientia. Series B. (English Edition)

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publication date

12 October 2022

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zbMATH Keywords

stabilization

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Heegaard genus

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Heegaard distance

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MaRDI profile type

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full work available at URL

https://doi.org/10.1007/s10473-022-0612-z

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The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).

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Connected sums of unstabilized Heegaard splittings are unstabilized

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Stabilizing and destabilizing Heegaard splittings of sufficiently complicated 3-manifolds

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An alternative proof that 3-manifolds can be triangulated

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Scindements de Heegaard des Variétés de Seifert Elliptiques et Euclidiennes

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Scindements de Heegaard des espaces lenticulaires

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On the Heegaard splitting of the torus \(T^ 3\)

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Heegaard genus of closed orientable Seifert 3-manifolds

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Reducing Heegaard splittings

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On the classification of Heegaard splittings

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Dehn surgery on knots

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The mapping class groups of reducible Heegaard splittings of genus two

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A note on Heegaard splittings of amalgamated 3-manifolds

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Links with Unlinking Number One are Prime

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The lens space realization problem

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Heegaard splittings of Haken manifolds have bounded distance.

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3-manifolds as viewed from the curve complex

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Stabilization of Heegaard splittings

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Heegaard splittings of distance exactly \(n\)

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Heegaard surfaces in Haken 3-manifolds

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Topology and combinatorics of 3-manifolds

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Stable functions and common stabilizations of Heegaard splittings

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Bounding the stable genera of Heegaard splittings from below

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Mapping class groups of medium distance Heegaard splittings

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Casson-Gordon's rectangle condition of Heegaard diagrams and incompressible tori in 3-manifolds

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A CONSTRUCTION OF ARBITRARILY HIGH DEGENERATION OF TUNNEL NUMBERS OF KNOTS UNDER CONNECTED SUM

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Knot exteriors with additive Heegaard genus and Morimoto's conjecture

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The amalgamation of high distance Heegaard splittings is always efficient

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Separating incompressible surfaces and stabilizations of Heegaard splittings

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The Rubinstein-Scharlemann graphic of a 3-manifold as the discriminant set of a stable map

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The Heegaard genus of amalgamated 3-manifolds

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On stability of Heegaard splittings

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Heegaard surfaces and measured laminations, II: Non-Haken 3–manifolds

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Heegaard surfaces and measured laminations. I: the Waldhausen conjecture

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Heegaard surfaces and the distance of amalgamation

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Saddle tangencies and the distance of Heegaard splittings

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Rank and genus of 3-manifolds

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On the degeneration of tunnel numbers under a connected sum

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A representation of orientable combinatorial 3-manifolds

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Geometry of the complex of curves. I: Hyperbolicity

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Geometry of the complex of curves. II: Hierarchical structure

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High distance knots

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Non degenerating Dehn fillings on genus two Heegaard splittings of knots' complements

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A Unique Decomposition Theorem for 3-Manifolds

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Irreducible Heegaard splittings of Seifert fibered spaces are either vertical or horizontal

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Affine structures in 3-manifolds. V: The triangulation theorem and Hauptvermutung

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There are Knots whose Tunnel Numbers go down under Connected Sum

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On the super additivity of tunnel number of knots

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Big Heegaard distance implies finite mapping class group

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Heegaard splittings and pseudo-Anosov maps

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Knot Floer homology detects fibred knots

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Every Two-Generator Knot is Prime

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A proof of the Gordon conjecture

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The Heegaard distances cover all nonnegative integers

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\(3\)-manifolds admitting locally large distance \(2\) Heegaard splittings

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Zur dreidimensionalen Topologie

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Comparing Heegaard splittings of non-Haken 3-manifolds

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Comparing Heegaard splittings -the bounded case

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Proximity in the curve complex: boundary reduction and bicompressible surfaces

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Heegaard splittings of \((\text{surface})\times I\) are standard

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Thin position and Heegaard splittings of the 3-sphere

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The tunnel number of the sum of \(n\) knots is at least \(n\)

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Annuli in generalized Heegaard splittings and degeneration of tunnel number

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Alternate Heegaard genus bounds distance

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A lower bound on tunnel number degeneration

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The Classification of Heegaard Splittings for (Compact Orient Able Surface) × <i>S<sup>1</sup> </i>

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The stabilization problem for Heegaard splittings of Seifert fibered spaces

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Additivity of tunnel number for small knots

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On the geometric and the algebraic rank of graph manifolds

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An infinite collection of Heegaard splittings that are equivalent after one stabilization

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Three-Dimensional Manifolds and Their Heegaard Diagrams

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Three dimensional manifolds, Kleinian groups and hyperbolic geometry

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On irreducible 3-manifolds which are sufficiently large

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Heegaard-Zerlegungen der 3-Sphäre

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Modifications and Cobounding Manifolds

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On amalgamations of Heegaard splittings with high distance

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Infinitely many hyperbolic 3-manifolds admitting distance-\(d\) and genus-\(g\) Heegaard splittings

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Finiteness of mapping class groups: locally large strongly irreducible Heegaard splittings

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Identifiers

Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S10473-022-0612-Z

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Sitelinks

Mathematics(1 entry)

mardi Publication:2080984

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