Quantum Invariants: A Study of Knot, 3-Manifolds, and Their Sets
Tomotada Ohtsuki
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, in other words, 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.
种类:
年:
2002
出版:
1st
出版社:
World Scientific Publishing Company
语言:
english
页:
508
ISBN 10:
9810246757
系列:
Series on Knots and Everything 29
文件:
PDF, 6.43 MB
IPFS:
,
english, 2002