scholarly journals Special Heegaard diagrams and the Kirby calculus

1990 ◽  
Vol 37 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Eduardo Rêgo ◽  
Eugénia César de Sá
Keyword(s):  
Heegaard Diagrams ◽  
Kirby Calculus

Kirby calculus

1999 ◽  
pp. 139-196 ◽  
Author(s):  
Robert Gompf ◽  
András Stipsicz
Keyword(s):  
Kirby Calculus

scholarly journals Refined Kirby calculus for integral homology spheres

2006 ◽  
Vol 10 (3) ◽  
pp. 1285-1317 ◽  
Author(s):  
Kazuo Habiro
Keyword(s):  
Integral Homology ◽  
Kirby Calculus

scholarly journals On Kirby calculus for null-homotopic framed links in 3–manifolds

2014 ◽  
Vol 14 (1) ◽  
pp. 115-134 ◽  
Author(s):  
Kazuo Habiro ◽  
Tamara Widmer
Keyword(s):  
Kirby Calculus

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    

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