This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The Chern-Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants.
eBook - PDF
Quantum Invariants: A Study Of Knots, 3-manifolds, And Their Sets
A Study of Knots, 3-Manifolds, and Their Sets
- 508 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Quantum Invariants: A Study Of Knots, 3-manifolds, And Their Sets
A Study of Knots, 3-Manifolds, and Their Sets
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Table of contents
- Contents
- Preface
- Chapter 1 Knots and polynomial invariants
- Chapter 2 Braids and representations of the braid groups
- Chapter 3 Operator invariants of tangles via sliced diagrams
- Chapter 4 Ribbon Hopf algebras and invariants of links
- Chapter 5 Monodromy representations of the braid groups derived from the Knizhnik-Zamolodchikov equation
- Chapter 6 The Kontsevich invariant
- Chapter 7 Vassiliev invariants
- Chapter 8 Quantum invariants of 3-manifolds
- Chapter 9 Perturbative invariants of knots and 3-manifolds
- Chapter 10 The LMO invariant
- Chapter 11 Finite type invariants of integral homology 3-spheres
- Appendix A The quantum group Uq(sl2)
- Appendix B The quantum sl3 invariant via a linear skein
- Appendix C Braid representations for the Alexander polynomial
- Appendix D Associators
- Appendix E Claspers
- Appendix F Physical background
- Appendix G Computations for the perturbative invariant
- Appendix H The quantum sl2 invariant and the Kauffman bracket
- Bibliography
- Notation
- Index
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Yes, you can access Quantum Invariants: A Study Of Knots, 3-manifolds, And Their Sets by Tomotada Ohtsuki in PDF and/or ePUB format, as well as other popular books in Biological Sciences & Science General. We have over 1.5 million books available in our catalogue for you to explore.