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Knots, Links and Their Invariants: An Elementary Course in Contemporary Knot Theory
 
A. B. Sossinsky Independent University of Moscow, Moscow, Russia and Poncelete Laboratory IUM-CNRS, Moscow, Russia
Softcover ISBN:  978-1-4704-7151-4
Product Code:  STML/101
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
eBook ISBN:  978-1-4704-7311-2
Product Code:  STML/101.E
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
Softcover ISBN:  978-1-4704-7151-4
eBook: ISBN:  978-1-4704-7311-2
Product Code:  STML/101.B
List Price: $118.00 $88.50
Sale Price: $70.80 $53.10
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Knots, Links and Their Invariants: An Elementary Course in Contemporary Knot Theory
A. B. Sossinsky Independent University of Moscow, Moscow, Russia and Poncelete Laboratory IUM-CNRS, Moscow, Russia
Softcover ISBN:  978-1-4704-7151-4
Product Code:  STML/101
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
eBook ISBN:  978-1-4704-7311-2
Product Code:  STML/101.E
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
Softcover ISBN:  978-1-4704-7151-4
eBook ISBN:  978-1-4704-7311-2
Product Code:  STML/101.B
List Price: $118.00 $88.50
Sale Price: $70.80 $53.10
  • Book Details
     
     
    Student Mathematical Library
    Volume: 1012023; 129 pp
    MSC: Primary 55; 51; 20

    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.

    Readership

    Undergraduate and graduate students interested in knot theory.

  • Table of Contents
     
     
    • Chapters
    • 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
  • Additional Material
     
     
  • Reviews
     
     
    • I found [this] book informative and interesting. It has the potential to encourage any beginner in low-dimensional topology to study knot theory. Thus, I strongly recommend this book as one of the elementary course books in knot theory.

      Santanu Acharjee, MathSciNet
    • This new addition to the Student Mathematical Library is an excellent concise introduction to knot theory and some of its associated algebra and topology. It is written clearly and simply, and well illustrated with many figures...Altogether, this book is ideal for self-study by undergraduates with an interest in topology.

      John Stillwell (University of San Francisco), Notices of the AMS
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1012023; 129 pp
MSC: Primary 55; 51; 20

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.

Readership

Undergraduate and graduate students interested in knot theory.

  • Chapters
  • 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
  • I found [this] book informative and interesting. It has the potential to encourage any beginner in low-dimensional topology to study knot theory. Thus, I strongly recommend this book as one of the elementary course books in knot theory.

    Santanu Acharjee, MathSciNet
  • This new addition to the Student Mathematical Library is an excellent concise introduction to knot theory and some of its associated algebra and topology. It is written clearly and simply, and well illustrated with many figures...Altogether, this book is ideal for self-study by undergraduates with an interest in topology.

    John Stillwell (University of San Francisco), Notices of the AMS
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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