{"product_id":"introduction-to-vassiliev-knot-invariants-hardback-9781107020832","title":"Introduction to Vassiliev Knot Invariants (Hardback) 9781107020832","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eIntroduction to Vassiliev Knot Invariants\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA detailed exposition of the theory with an emphasis on its combinatorial aspects.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eS. Chmutov (Author), S. Duzhin (Author), J. Mostovoy (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107020832, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 24 May 2012\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e520 pages, 430 b\/w illus.  15 tables  375 exercises\u003cbr\u003e25.3 x 17.7 x 3 cm, 1.08 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'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\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eWith 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Knots and their relatives\u003cbr\u003e 2. Knot invariants\u003cbr\u003e 3. Finite type invariants\u003cbr\u003e 4. Chord diagrams\u003cbr\u003e 5. Jacobi diagrams\u003cbr\u003e 6. Lie algebra weight systems\u003cbr\u003e 7. Algebra of 3-graphs\u003cbr\u003e 8. The Kontsevich integral\u003cbr\u003e 9. Framed knots and cabling operations\u003cbr\u003e 10. The Drinfeld associator\u003cbr\u003e 11. The Kontsevich integral: advanced features\u003cbr\u003e 12. Braids and string links\u003cbr\u003e 13. Gauss diagrams\u003cbr\u003e 14. Miscellany\u003cbr\u003e 15. The space of all knots\u003cbr\u003e Appendix\u003cbr\u003e References\u003cbr\u003e Notations\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Geometry [\u003ca title=\"See our other books on Geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Geometry%20%5BPBM%5D%22\"\u003ePBM\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46004866547992,"sku":"9781107020832","price":65.37,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107020832i_8c33b7ec-6c47-49ef-86f1-8e7edf494449.jpg?v=1691361105","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/introduction-to-vassiliev-knot-invariants-hardback-9781107020832","provider":"Freshly Printed Books","version":"1.0","type":"link"}