LEADER 04396nam 22005535 450 001 9910338251803321 005 20200702064810.0 010 $a3-030-05213-3 024 7 $a10.1007/978-3-030-05213-3 035 $a(CKB)4100000008103747 035 $a(MiAaPQ)EBC5771236 035 $a(DE-He213)978-3-030-05213-3 035 $a(PPN)236522604 035 $a(EXLCZ)994100000008103747 100 $a20190504d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn Introduction to Quantum and Vassiliev Knot Invariants /$fby David M. Jackson, Iain Moffatt 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (425 pages) 225 1 $aCMS Books in Mathematics, Ouvrages de mathématiques de la SMC,$x1613-5237 311 $a3-030-05212-5 327 $aPart I Basic Knot Theory -- Knots -- Knot and Link Invariants -- Framed Links -- Braids and the Braid Group -- Part II Quantum Knot Invariants -- R-Matrix Representations of Bn -- Knot Invariants through R-Matrix Representations of Bn -- Operator Invariants -- Ribbon Hopf Algebras -- Reshetikin-Turaev Invariants -- Part III Vassiliev Invarients -- The Fundamentals of Vassiliev Invariants -- Chord Diagrams -- Vassiliev Invariants of Framed Knots -- Jacobi Diagrams -- Lie Algebra Weight Systems -- Part IV The Kontsevich Invariant -- q-tangles -- Jacobi Diagrams on a 1-manifold -- A Construction of the Kontsevich Invariant -- Universality Properties of the Kontsevich Invariant -- Appendix A Background on Modules and Linear Algebra -- Appendix B Rewriting the Definition of Operator Invariants -- Appendix C Computations in Quasi-triangular Hopf Algebras -- Appendix D The Ribbon Hopf Algebra -- Appendix E A Proof of the Invariance of the Reshetikin-Turaev Invariants. 330 $aThis book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant. 410 0$aCMS Books in Mathematics, Ouvrages de mathématiques de la SMC,$x1613-5237 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aNonassociative rings 606 $aRings (Algebra) 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aNon-associative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11116 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 0$aNonassociative rings. 615 0$aRings (Algebra). 615 14$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aNon-associative Rings and Algebras. 676 $a514.224 676 $a530.143 700 $aJackson$b David M$4aut$4http://id.loc.gov/vocabulary/relators/aut$0210514 702 $aMoffatt$b Iain$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910338251803321 996 $aAn Introduction to Quantum and Vassiliev Knot Invariants$92507102 997 $aUNINA