Knots, Links and Their Invariants
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Knots, Links and Their Invariants: An Elementary Course in Contemporary Knot Theory(Student Mathematical Library)

Knots, Links and Their Invariants: An Elementary Course in Contemporary Knot Theory(Student Mathematical Library)


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About the Book

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.

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

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


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Product Details
  • ISBN-13: 9781470471514
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Height: 216 mm
  • No of Pages: 142
  • Sub Title: An Elementary Course in Contemporary Knot Theory
  • ISBN-10: 1470471515
  • Publisher Date: 08 Jul 2023
  • Binding: Paperback
  • Language: English
  • Series Title: Student Mathematical Library
  • Width: 127 mm


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