scholarly journals HEEGAARD DIAGRAMS FOR CLOSED 4-MANIFOLDS

1979 ◽  
pp. 219-237 ◽  
Author(s):  
José María Montesinos
Keyword(s):  
Heegaard Diagrams

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.

scholarly journals Heegaard diagrams and optimal Morse flows on non-orientable 3-manifolds of genus 1 and genus $2$

2020 ◽  
Vol 13 (3) ◽  
pp. 33-48
Author(s):  
Christian Hatamian ◽  
Alexandr Prishlyak
Keyword(s):  
Closed Surface ◽  
Singular Points ◽  
Topological Properties ◽  
Heegaard Diagrams ◽  
Genus 2

The present paper investigates Heegaard diagrams of non-orientable closed $3$-manifolds, i.e. a non-orienable closed surface together with two sets of meridian disks of both handlebodies. It is found all possible non-orientable genus $2$ Heegaard diagrams of complexity less than $6$. Topological properties of Morse flows on closed smooth non-orientable $3$-manifolds are described. Normalized Heegaard diagrams are furhter used for classification Morse flows with a minimal number of singular points and singular trajectories    

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 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.

scholarly journals Heegaard diagrams corresponding to Turaev surfaces

2015 ◽  
Vol 24 (04) ◽  
pp. 1550026 ◽  
Author(s):  
Cody Armond ◽  
Nathan Druivenga ◽  
Thomas Kindred
Keyword(s):  
Heegaard Diagrams ◽  
Link Diagrams

We describe a correspondence between Turaev surfaces of link diagrams on S2 ⊂ S3 and special Heegaard diagrams for S3 adapted to links.

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.

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