scholarly journals Small 3-manifolds with large Heegaard distance

2013 ◽  
Vol 155 (3) ◽  
pp. 431-441 ◽  
Author(s):  
TAO LI
Keyword(s):  
Large Distance ◽  
Heegaard Splitting ◽  
Heegaard Distance

AbstractWe construct examples of closed non-Haken hyperbolic 3-manifolds with a Heegaard splitting of arbitrarily large distance.

scholarly journals Heegaard distance of the link complements in S3

2021 ◽  
pp. 2150005
Author(s):  
Xifeng Jin
Keyword(s):  
Heegaard Splitting ◽  
Link Complements ◽  
Genus Formula ◽  
Heegaard Distance ◽  
Distance Formula

We show that, for any integers, [Formula: see text] and [Formula: see text], there exists a link in [Formula: see text] such that its complement has a genus [Formula: see text] Heegaard splitting with distance [Formula: see text].

scholarly journals Many Haken Heegaard splittings

2018 ◽  
Vol 12 (02) ◽  
pp. 357-369
Author(s):  
Alessandro Sisto
Keyword(s):  
Hyperbolic Manifolds ◽  
Heegaard Splitting ◽  
Heegaard Splittings ◽  
Simple Criterion ◽  
Heegaard Genus ◽  
Heegaard Distance ◽  
The Way

We give a simple criterion for a Heegaard splitting to yield a Haken manifold. As a consequence, we construct many Haken manifolds, in particular homology spheres, with prescribed properties, namely Heegaard genus, Heegaard distance and Casson invariant. Along the way we give simpler and shorter proofs of the existence of splittings with specified Heegaard distance, originally proven by Ido–Jang–Kobayashi, of the existence of hyperbolic manifolds with prescribed Casson invariant, originally due to Lubotzky–Maher–Wu, and of a result about subsurface projections of disc sets (for which we even get better constants), originally due to Masur–Schleimer.

scholarly journals Some Sufficient Conditions for Heegaard Genera to Be Additive Under Annulus Sum

2014 ◽  
Vol 115 (2) ◽  
pp. 173 ◽  
Author(s):  
Fengling Li ◽  
Fengchun Lei ◽  
Guoqiu Yang
Keyword(s):  
Sufficient Conditions ◽  
Heegaard Splitting ◽  
Heegaard Distance

Let $M_{i}$ be a compact orientable 3-manifold, and $A_{i}$ an incompressible annulus on a component $F_i$ of $\partial M_i$, $i=1,2$. Suppose $A_{1}$ is separating on $F_{1}$ and $A_{2}$ is non-separating on $F_{2}$. Let $M$ be the annulus sum of $M_1$ and $M_2$ along $A_1$ and $A_2$. In the present paper we show that if $M_{i}$ has a Heegaard splitting $V_{i}\cup_{S_{i}}W_{i}$ with Heegaard distance $d(S_{i})\geq2g(M_{i})+5$ for $i=1,2$, then $g(M)=g(M_{1})+g(M_{2})$. Moreover, when $g(F_{2})\geq 2$, the minimal Heegaard splitting of $M$ is unique up to isotopy.

scholarly journals DETECTING TORSION IN SKEIN MODULES USING HOCHSCHILD HOMOLOGY

2006 ◽  
Vol 15 (02) ◽  
pp. 259-277 ◽  
Author(s):  
MICHAEL McLENDON
Keyword(s):  
Tensor Product ◽  
Spectral Sequence ◽  
Boundary Surface ◽  
Hochschild Homology ◽  
Heegaard Splitting ◽  
Common Boundary ◽  
Skein Modules ◽  
Skein Module ◽  
Hochschild Complex

Given a Heegaard splitting of a closed 3-manifold, the skein modules of the two handlebodies are modules over the skein algebra of their common boundary surface. The zeroth Hochschild homology of the skein algebra of a surface with coefficients in the tensor product of the skein modules of two handlebodies is interpreted as the skein module of the 3-manifold obtained by gluing the two handlebodies together along this surface. A spectral sequence associated to the Hochschild complex is constructed and conditions are given for the existence of algebraic torsion in the completion of the skein module of this 3-manifold.

Een alternatieve benadering voor herontwerp van werk

2013 ◽  
Vol 26 (1) ◽  
Author(s):  
Gemma M.C. van Ruitenbeek ◽  
Marike J.G.P. Mulder ◽  
Fred R.H. Zijlstra ◽  
Frans J.N. Nijhuis ◽  
Henny P.G. Mulders
Keyword(s):  
Labour Market ◽  
Large Distance ◽  
People With Disabilities ◽  
Work Capacity ◽  
Healthcare Organization ◽  
Work Processes ◽  
Large Group ◽  
Work Redesign ◽  
Underlying Principle ◽  
Alternative Approach

An alternative approach for work redesign: experiences with the method ‘Inclusive Redesign of Work Processes’ (Dutch abbreviation: IHW) An alternative approach for work redesign: experiences with the method ‘Inclusive Redesign of Work Processes’ (Dutch abbreviation: IHW) This article introduces an alternative approach to work redesign: the method ‘Inclusive Redesign of Work Processes’ (Dutch abbreviation: IHW-method), aimed to make it possible to participate in the labour market for people with a large distance to the labour market. The IHW-method is based on an analysis and redesign of work processes which subsequently allows organizing work processes in such a way that jobs can be created for people with limited capabilities. The underlying principle is task differentiation from the perspective of worker’s capabilities, allowing organizations to make optimal use of all the existing work capacity and talent in the labour market. This article presents the underlying ideas and background for the development of the method IHW. The redesign principles of the method IHW and the first experiences with this method in a healthcare organization are discussed. The method turned out to be effective for the creation of suitable work for a large group of people with disabilities in this organization.

Local uniqueness of certain geodesics related to Heegaard splittings

2018 ◽  
Vol 27 (09) ◽  
pp. 1842003
Author(s):  
Liang Liang ◽  
Fengling Li ◽  
Fengchun Lei ◽  
Jie Wu
Keyword(s):  
Heegaard Splitting ◽  
Sufficient Condition ◽  
Heegaard Splittings ◽  
Local Uniqueness ◽  
Uniqueness Property

Suppose [Formula: see text] is a Heegaard splitting and [Formula: see text] is an essential separating disk in [Formula: see text] such that a component of [Formula: see text] is homeomorphic to [Formula: see text], [Formula: see text]. In this paper, we prove that if there is a locally complicated simplicial path in [Formula: see text] connecting [Formula: see text] to [Formula: see text], then the geodesic connecting [Formula: see text] to [Formula: see text] is unique. Moreover, we give a sufficient condition such that [Formula: see text] is keen and the geodesic between any pair of essential disks on the opposite sides has local uniqueness property.

The Effect of Froude Number on Entrainment in Two-Dimensional Line Plumes

1981 ◽  
Vol 103 (3) ◽  
pp. 471-477 ◽  
Author(s):  
W. F. Phillips
Keyword(s):  
Froude Number ◽  
Large Distance ◽  
Universal Constant ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Development Length ◽  
High Discharge ◽  
Entrainment Coefficient ◽  
Theoretical Results

Theoretical results are presented which predict the entrainment coefficient in a forced plume as a function of the local Froude number. The model does not require any external specification of the velocity and temperature profiles. The Froude number for any plume, in a motionless isothermal ambient, approaches a universal constant, at a large distance above the source. However, it is shown here that the development length for the Froude number, in plumes with high discharge Froude number, is of the order of a few hundred times the discharge width.

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