Quantum Invariants: A Study Of Knots, 3-manifolds, And Their Sets
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Quantum Invariants: A Study Of Knots, 3-manifolds, And Their Sets

A Study of Knots, 3-Manifolds, and Their Sets

  1. 508 pages
  2. English
  3. PDF
  4. 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
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About This Book

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.

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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 one million books available in our catalogue for you to explore.

Information

Publisher
World Scientific
Year
2001
ISBN
9789812811172
Topic
Biological Sciences
Subtopic
Science General
Index
Biological Sciences

Table of contents

  1. Contents
  2. Preface
  3. Chapter 1 Knots and polynomial invariants
  4. Chapter 2 Braids and representations of the braid groups
  5. Chapter 3 Operator invariants of tangles via sliced diagrams
  6. Chapter 4 Ribbon Hopf algebras and invariants of links
  7. Chapter 5 Monodromy representations of the braid groups derived from the Knizhnik-Zamolodchikov equation
  8. Chapter 6 The Kontsevich invariant
  9. Chapter 7 Vassiliev invariants
  10. Chapter 8 Quantum invariants of 3-manifolds
  11. Chapter 9 Perturbative invariants of knots and 3-manifolds
  12. Chapter 10 The LMO invariant
  13. Chapter 11 Finite type invariants of integral homology 3-spheres
  14. Appendix A The quantum group Uq(sl2)
  15. Appendix B The quantum sl3 invariant via a linear skein
  16. Appendix C Braid representations for the Alexander polynomial
  17. Appendix D Associators
  18. Appendix E Claspers
  19. Appendix F Physical background
  20. Appendix G Computations for the perturbative invariant
  21. Appendix H The quantum sl2 invariant and the Kauffman bracket
  22. Bibliography
  23. Notation
  24. Index