CMS Books in Mathematics

An Introduction to Quantum and Vassiliev Knot Invariants

Authors: Jackson, David M, Moffatt, Iain

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  • Introduces key concepts and constructions both diagrammatic and algebraic in the field
  • Exemplifies aspects of problem solving approaches inherent in mathematics
  • Demonstrates a range of mathematical concepts tangibly through instantiations in context
  • Exposes reader to foundations and applications of mathematical constructions
  • Provides exercises throughout text
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eBook $89.00
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  • ISBN 978-3-030-05213-3
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Hardcover $119.99
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About this book

This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant.


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Reviews

 “This text is a comprehensive and well written introduction to quantum and Vassiliev invariants of knots. … There is sufficient detail for students and exercises. The text is also an excellent reference for researchers interested in quantum and Vassiliev invariants.” (Heather A. Dye, zbMATH 1425.57007, 2019)
 

Table of contents (18 chapters)

Table of contents (18 chapters)

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-3-030-05213-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover $119.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
An Introduction to Quantum and Vassiliev Knot Invariants
Authors
Series Title
CMS Books in Mathematics
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-05213-3
DOI
10.1007/978-3-030-05213-3
Hardcover ISBN
978-3-030-05212-6
Series ISSN
1613-5237
Edition Number
1
Number of Pages
XX, 422
Number of Illustrations
561 b/w illustrations
Topics