scholarly journals A note on irreducible Heegaard diagrams

2006 ◽  
Vol 2006 ◽  
pp. 1-11
Author(s):  
Alberto Cavicchioli ◽  
Fulvia Spaggiari
Keyword(s):  
Alternative Proof ◽  
Heegaard Diagrams ◽  
The Real ◽  
Connected Sums ◽  
Heegaard Diagram ◽  
Simple Alternative

We construct a Heegaard diagram of genus three for the real projective 3-space, which has no waves and pairs of complementary handles. The first example was given by Im and Kim but our diagram has smaller complexity. Furthermore the proof presented here is quite different to that of the quoted authors, and permits also to obtain a simple alternative proof of their result. Examples of irreducible Heegaard diagrams of certain connected sums complete the paper.

scholarly journals An irreducible Heegaard diagram of the real projective 3-spacep3

2000 ◽  
Vol 23 (2) ◽  
pp. 123-129 ◽  
Author(s):  
Young Ho Im ◽  
Soo Hwan Kim
Keyword(s):  
Projective Space ◽  
Real Projective Space ◽  
Heegaard Diagrams ◽  
The Real ◽  
Heegaard Diagram ◽  
Genus 2

We give a genus 3 Heegaard diagramHof the real projective spacep3, which has no waves and pairs of complementary handles. So Negami's result that every genus 2 Heegaard diagram ofp3is reducible cannot be extended to Heegaard diagrams ofp3with genus 3.

DECOMPOSITIONS OF PLANAR HOMEOMORPHISMS USING COMPUTER SOFTWARE

2002 ◽  
Vol 11 (06) ◽  
pp. 955-972
Author(s):  
IL YEUN CHO ◽  
MITSUYUKI OCHIAI ◽  
YOSHIKO SAKATA
Keyword(s):  
Data Structure ◽  
Computer Software ◽  
The Self ◽  
Heegaard Diagrams ◽  
Heegaard Diagram ◽  
Connected Surface

We have established in [S3] an algorithm with a new data structure that decomposes gluing homeomorphisms of 3-manifolds given by planar Heegaard diagrams into a product of canonical Dehn's twists. To support this study, we developed a computer software called Decomposition of Planar Homeomorphisms (Genus 3) that automatically decomposes the self homeomorphis of a closed connected surface given by any planar Heegaard diagram of genus 3 into a product of canonical Dehn's twists. In this paper, we demonstrate the content and the implementation that this software holds and also show its availability.

An equivalent description of the lens space L(p,q) with p prime

2020 ◽  
Vol 29 (10) ◽  
pp. 2042005
Author(s):  
Fengling Li ◽  
Dongxu Wang ◽  
Liang Liang ◽  
Fengchun Lei
Keyword(s):  
Complete System ◽  
Lens Space ◽  
Heegaard Splitting ◽  
Prime Integer ◽  
Heegaard Diagrams ◽  
Heegaard Diagram ◽  
Genus Formula ◽  
Equivalent Description

In the paper, we give an equivalent description of the lens space [Formula: see text] with [Formula: see text] prime in terms of any corresponding Heegaard diagrams as follows: Let [Formula: see text] be a closed orientable 3-manifold with [Formula: see text] and [Formula: see text] a Heegaard splitting of genus [Formula: see text] for [Formula: see text] with an associated Heegaard diagram [Formula: see text]. Assume [Formula: see text] is a prime integer. Then [Formula: see text] is homeomorphic to the lens space [Formula: see text] if and only if there exists an embedding [Formula: see text] such that [Formula: see text] bounds a complete system of surfaces for [Formula: see text].

scholarly journals A simple proof of a result of Iglehart and Shedler

1985 ◽  
Vol 17 (1) ◽  
pp. 239-241
Author(s):  
Mark Berman
Keyword(s):  
Confidence Intervals ◽  
Simple Proof ◽  
Passage Time ◽  
Alternative Proof ◽  
Multiclass Networks ◽  
Simple Alternative ◽  
General Service Times ◽  
Service Times ◽  
General Service ◽  
Networks Of Queues

Iglehart and Shedler (1983) prove that the ‘labelled jobs’ method for estimation of passage-time characteristics in closed multiclass networks of queues with general service times provides asymptotically shorter confidence intervals than does the ‘marked job’ method. A simple alternative proof of this result, under slightly more restrictive conditions, is given here.

scholarly journals CONSTRUCTING DOUBLY-POINTED HEEGAARD DIAGRAMS COMPATIBLE WITH (1,1) KNOTS

2013 ◽  
Vol 22 (11) ◽  
pp. 1350071
Author(s):  
PHILIP ORDING
Keyword(s):  
Normal Form ◽  
Floer Homology ◽  
Solid Torus ◽  
Heegaard Splitting ◽  
Heegaard Diagrams ◽  
Homology Groups ◽  
Knot Floer Homology ◽  
Heegaard Diagram ◽  
Train Tracks

A (1,1) knot K in a 3-manifold M is a knot that intersects each solid torus of a genus 1 Heegaard splitting of M in a single trivial arc. Choi and Ko developed a parametrization of this family of knots by a four-tuple of integers, which they call Schubert's normal form. This paper presents an algorithm for constructing a genus 1 doubly-pointed Heegaard diagram compatible with K, given a Schubert's normal form for K. The construction, coupled with results of Ozsváth and Szabó, provides a practical way to compute knot Floer homology groups for (1,1) knots. The construction uses train tracks, and its method is inspired by the work of Goda, Matsuda, and Morifuji.

scholarly journals A Simple Proof That Generic 3-RPR Manipulators Have Two Aspects

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Michel Coste
Keyword(s):  
Free Path ◽  
Simple Proof ◽  
Singular Locus ◽  
Parallel Robot ◽  
Alternative Proof ◽  
Connected Components ◽  
Theoretical Studies ◽  
Geometric Properties ◽  
Simple Alternative ◽  
Planar Robots

Avoiding singularities in the workspace of a parallel robot is an important issue. The case of 3-RPR planar robots is an important subject of theoretical studies. We study the singularities of planar 3-RPR robots by using a new parameterization of the singular locus in a modified workspace. This approach enables us to give a simple alternative proof of a result recently proved by Husty: the complement of the singular locus in the workspace of a generic 3-RPR manipulator has two connected components (called aspects); we also give a procedure to design a singularity-free path connecting any two points in the same aspect. The parameterization introduced in this paper, due to its simple geometric properties, proves to be useful for the study of the singularities of 3-RPR robots.

scholarly journals On the Bernstein Problem in the Three-dimensional Heisenberg Group

2016 ◽  
Vol 59 (01) ◽  
pp. 50-61
Author(s):  
Josef F. Dorfmeister ◽  
Jun-ichi Inoguchi ◽  
Shimpei Kobayashi
Keyword(s):  
Heisenberg Group ◽  
Three Dimensional ◽  
Loop Group ◽  
Alternative Proof ◽  
Geometric Meaning ◽  
Bernstein Problem ◽  
Minimal Graphs ◽  
Simple Alternative ◽  
Two Parameter ◽  
Group Technique

Abstract In this note we present a simple alternative proof for the Bernstein problem in the threedimensional Heisenberg group Nil3 by using the loop group technique. We clarify the geometric meaning of the two-parameter ambiguity of entire minimal graphs with prescribed Abresch- Rosenberg diòerential.

scholarly journals A simple proof of a result of Iglehart and Shedler

1985 ◽  
Vol 17 (01) ◽  
pp. 239-241
Author(s):  
Mark Berman
Keyword(s):  
Confidence Intervals ◽  
Simple Proof ◽  
Passage Time ◽  
Alternative Proof ◽  
Multiclass Networks ◽  
Simple Alternative ◽  
General Service Times ◽  
Service Times ◽  
General Service ◽  
Networks Of Queues

Iglehart and Shedler (1983) prove that the ‘labelled jobs’ method for estimation of passage-time characteristics in closed multiclass networks of queues with general service times provides asymptotically shorter confidence intervals than does the ‘marked job’ method. A simple alternative proof of this result, under slightly more restrictive conditions, is given here.

scholarly journals Derivations on commutative operator algebras

1985 ◽  
Vol 32 (3) ◽  
pp. 415-418
Author(s):  
Mark Spivack
Keyword(s):  
Hilbert Space ◽  
Banach Spaces ◽  
Von Neumann Algebra ◽  
Operator Algebras ◽  
Bounded Operator ◽  
Alternative Proof ◽  
Reflexive Banach Spaces ◽  
Von Neumann ◽  
Simple Alternative

It is well-known that any derivation on a commutative von Neumann algebra is implemented by a bounded operator. In this note we present a simple alternative proof, which generalizes the result further within Hilbert space, and to reflexive Banach spaces.

An alternative proof of doubly transitive property of a connected quandle of a prime order

2015 ◽  
Vol 24 (01) ◽  
pp. 1520001 ◽  
Author(s):  
Taisuke Watanabe
Keyword(s):  
Prime Order ◽  
Alternative Proof ◽  
Simple Alternative ◽  
Transitive Property

In this paper, we study doubly transitive property of a connected quandle of a prime order. In 2011, Ferman, Nowik and Teicher proved that the group of all quandle automorphisms of a connected quandle of a prime order acts sharply doubly transitively on itself. In this paper, we give a simple alternative proof.

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