Quantum and related invariants of knots and 3-manifolds are presented, and polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants derived from the representation of quantum groups and the monodromy of solutions to the Knizhnik-Zamolodchikov equation. Discussion encompasses the Kontsevich invariants, the theory of Vassiliev invariants, the LMO invariants, and finite type invariants of 3-manifolds. The Chern- Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants. The author is affiliated with the Tokyo Institute of Technology, Japan. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Quantum Invariants: A Study of Knot, 3-Manifolds, and Their Sets
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Uncover the secrets of quantum knot invariants and 3-manifolds with this groundbreaking book from a Tokyo Institute of Technology expert.
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