David M. Jackson, Iain Moffatt

An Introduction to Quantum and Vassiliev Knot Invariants (eBook, PDF)

• Format: PDF

Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 422
• Erscheinungstermin: 4. Mai 2019
• Englisch
• ISBN-13: 9783030052133
• Artikelnr.: 56842463

Autorenporträt

  

Inhaltsangabe

Part 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.

Rezensionen

"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)