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OverviewThis 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. Full Product DetailsAuthor: David M. Jackson , Iain MoffattPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: 1st ed. 2019 Weight: 0.828kg ISBN: 9783030052126ISBN 10: 3030052125 Pages: 422 Publication Date: 16 May 2019 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of ContentsReviews“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)
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