Overview

One of the most significant unsolved problems in mathematics is the complete classification of knots. The main purpose of this text is to introduce the reader to the use of computer programming to obtain the table of knots. The author seeks to present this problem as clearly and methodically as possible, starting from the very basics. Mathematical ideas and concepts are extensively discussed, and no advance background is required.

Full Product Details

Author:   Charilaos N Aneziris (Brookhaven Nat'l Lab, Usa)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Volume:   20
Dimensions:   Width: 16.30cm , Height: 2.60cm , Length: 23.00cm
Weight:   0.685kg
ISBN:  

9789810238780

ISBN 10:   9810238789
Pages:   408
Publication Date:   14 December 1999
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you.

Table of Contents

A knot theory primer - a general understanding of topology; knot theory as a branch of topology; the regular representations of knots; the equivalence moves; the knot invariants; elements of group theory; the fundamental group; the knot group; the colourization invariants; the Alexander polynomial; the theory of linear homogeneous systems; calculating the Alexander polynomial; the minor Alexander polynomials; the Meridian-longitude invariants; proving a knot's chirality; braid theory - skein invariants; calculating the HOMFLYPT polynomials; knot theory after the HOMFLYPT; the problem of knot tabulation - basic concepts of computer programming; the Dowker notation; drawing the knot; when is a notation drawable?; the equal drawability moves; multiple notations for equivalent knots; ordering the Dowker notations; calculating the notation invariants; a few examples; the knot tabulation algorithm; the pseudocode; the flowchart; actual results; the table of knots.

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