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Knots, Links and Their Invariants A. B. Sossinsky

Knots, Links and Their Invariants By A. B. Sossinsky

Knots, Links and Their Invariants by A. B. Sossinsky


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Summary

Provides an elementary introduction to knot theory. Unlike many other books on knot theory, this has practically no prerequisites; it requires only basic plane and spatial Euclidean geometry but no knowledge of topology or group theory.

Knots, Links and Their Invariants Summary

Knots, Links and Their Invariants: An Elementary Course in Contemporary Knot Theory by A. B. Sossinsky

This book is an elementary introduction to knot theory. Unlike many other books on knot theory, this book has practically no prerequisites; it requires only basic plane and spatial Euclidean geometry but no knowledge of topology or group theory. It contains the first elementary proof of the existence of the Alexander polynomial of a knot or a link based on the Conway axioms, particularly the Conway skein relation. The book also contains an elementary exposition of the Jones polynomial, HOMFLY polynomial and Vassiliev knot invariants constructed using the Kontsevich integral. Additionally, there is a lecture introducing the braid group and shows its connection with knots and links.

Other important features of the book are the large number of original illustrations, numerous exercises and the absence of any references in the first eleven lectures. The last two lectures differ from the first eleven: they comprise a sketch of non-elementary topics and a brief history of the subject, including many references.

About A. B. Sossinsky

A. B. Sossinsky, Independent University of Moscow, Russia, and Poncelete Laboratory IUM-CNRS, Moscow, Russia.

Table of Contents

  • Knots and links, Reidmeister moves
  • The Conway polynomial
  • The arithemtic of knots
  • Some simple knot invariants
  • The Kauffman bracket
  • The Jones polynomial
  • Braids
  • Discriminants and finite type invariants
  • Vassiliev invariants
  • Combinatorial description of Vassiliev invariants
  • The Kontsevich integrals
  • Other important topics
  • A brief history of knot theory
  • Bibliography
  • Index

Additional information

NPB9781470471514
9781470471514
1470471515
Knots, Links and Their Invariants: An Elementary Course in Contemporary Knot Theory by A. B. Sossinsky
New
Paperback
American Mathematical Society
2023-07-08
142
N/A
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