With hundreds of worked examples, exercises and illustrations, this detailed exposition of the theory of Vassiliev knot invariants opens the field to students with little or no knowledge in this area. It also serves as a guide to more advanced material. The book begins with a basic and informal introduction to knot theory, giving many examples of knot invariants before the class of Vassiliev invariants is introduced. This is followed by a detailed study of the algebras of Jacobi diagrams and 3-graphs, and the construction of functions on these algebras via Lie algebras. The authors then describe two constructions of a universal invariant with values in the algebra of Jacobi diagrams: via iterated integrals and via the Drinfeld associator, and extend the theory to framed knots. Various other topics are then discussed, such as Gauss diagram formulae, before the book ends with Vassiliev's original construction.Read more
- Assumes no prior knowledge of knot theory
- Includes hundreds of worked examples, illustrations and exercises to suit graduate and undergraduate students
- Explores connections with graph theory, number theory, Lie algebras, group theory and algebraic topology to help readers understand the theory in context
Reviews & endorsements
'It is clear that this book is a labour of love, and that no effort has been spared in making it a useful textbook and reference for those seeking to understand its subject. The target readership consists both of first-time learners, for whom pedagogically sound explanations and numerous well-chosen exercises are provided to enhance comprehension, and of experienced mathematicians, for whom many tables of data and readable concise guides to research literature are provided. Numerous figures are included to supplement written explanations. The content is well-modularized, in the sense that different sections of the book may be read independently of one another, and that when there is an essential dependence between sections then this fact is clearly pointed out and the relationship between the sections is explained. This, and a thorough index, combine to make this book not only a valuable textbook, but also a valuable reference.' Zentralblatt MATHSee more reviews
'The book's excellent preface goes on to give an in embryo characterization of the objects in the title … As being a textbook - and an excellent one - the authors take us from a dense but accessible introduction to knots as such to quantum invariants, all in the first two chapters, and then go on to Vassiliev's finite type invariants. Then we get to chord diagrams, Lie algebra connections, Kontsevich's integral, work by Drinfeld, more stuff on the Kontsevich integral, material on braids, and more. The book closes with a chapter on '[t]he space of all knots'. It's very, very attractive material.' Michael Berg, MAA Reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: May 2012
- format: Hardback
- isbn: 9781107020832
- length: 520 pages
- dimensions: 253 x 177 x 30 mm
- weight: 1.08kg
- contains: 430 b/w illus. 15 tables 375 exercises
- availability: Available
Table of Contents
1. Knots and their relatives
2. Knot invariants
3. Finite type invariants
4. Chord diagrams
5. Jacobi diagrams
6. Lie algebra weight systems
7. Algebra of 3-graphs
8. The Kontsevich integral
9. Framed knots and cabling operations
10. The Drinfeld associator
11. The Kontsevich integral: advanced features
12. Braids and string links
13. Gauss diagrams
15. The space of all knots
Find resources associated with this titleYour search for '' returned .
Type Name Unlocked * Format Size
This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.
Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.
Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.
If you are having problems accessing these resources please contact firstname.lastname@example.org.
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email email@example.comRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.×