LinKnot- Knot Theory by Computer

by S. Jablan and R. Sazdanovic,

  Series on Knots and Everything Vol. 21,

World Scientific, Singapore.

          

Download of the Mathematica program LinKnot: http://www.mi.sanu.ac.rs/vismath/linknot/index.html

 

 

Contents 
 
 

     1.1 Preface

 

Chapter 1: Basic graph theory

   1.1 Basic graph theory

    1.2 Shadows of KLs

    1.2.1 Gauss and Dowker code

    1.3 KL diagrams

    1.4 Reidemeister moves

    1.5 Conway notation

    1.6 Classification of KLs

    1.7 LinKnot functions and KL notation

    1.8 Rational world and KL invariants

        1.8.1  Chirality of rational KLs

    1.9 Unlinking numbers

        1.9.1  Unlinking gap

    1.10 Prime and composite KLs

    1.11 Non-invertible KLs

        1.11.1  Tangle types

        1.11.2  Non-invertible pretzel knots

        1.11.3  Non-invertible arborescent knots

        1.11.4  Non-invertible polyhedral knots

    1.12 Braids

        1.12.1  KLs and braids

    1.13 Braid family representatives

        1.13.1  Applications of minimum braids and braid family representatives

    1.14 More KL invariants

    1.15 Borromean links
 
 

Chapter 2: Recognition and Generation of Knots and Links

    2.1 Recognition of KLs

        2.1.1  Group of KL

    2.2 Polynomial invariants

    2.3 Vassiliev invariants

    2.4 Derivation and classification of KLs

    2.5 Basic polyhedra and polyhedral KLs

    2.6 Basic polyhedra and non-algebraic tangles

        2.6.1  Generalized tangles

        2.6.2  n-tangles and basic polyhedra

        2.6.3  Non-algebraic tangle compositions and component algebra

    2.7 KL tables

        2.7.1  Non-alternating and almost alternating KLs

    2.8 Projections of KLs and chirality

    2.9 Families of undetectable KLs

    2.10 A dream- new KL tables
 
 

Chapter 3: History of Knot Theory and Certain Applications of Knots and Links

    3.1 History of knot theory

    3.2 Mirror curves

        3.2.1  Tamil treshold designs

        3.2.2  Tchokwe sand drawings

        3.2.3  Mirror curves

        3.2.4  Enumeration

        3.2.5  Lunda designs

        3.2.6  Polyominoes

            3.2.6.1  Lunda polyominoes and Lunda animals

        3.2.7  KLs and mirror curves

        3.2.8  Mirror curves on different surfaces

        3.2.9  Mirror curves in art

        3.2.10  KLs and self-avoiding curves

    3.3 KLs and fullerenes

        3.3.1  General fullerenes, graphs, symmetry and isomers

        3.3.2  5/6 fullerenes

        3.3.3  Knot theory and fullerenes

        3.3.4  Nanotubes, conical and biconical fullerenes and their symmetry

        3.3.5  Fullerenes on other surfaces

    3.4 KLs and logic

        3.4.1  Waveforms

        3.4.2  Knot automata

 

Appendix 


Bibliography


Index

LinKnot functions  

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