Quantum Invariants: A Study of Knots, 3-Manifolds, and Their Sets
Quantum Invariants: A Study of Knots, 3-Manifolds, and Their Sets
复制标题
量子不变量：结、3-流形及其集合的研究
作者：
T. Ohtsuki
这本书提供了一个广泛的和自我包含的介绍量子和相关的不变量的结和3流形。结的多项式不变量，例如琼斯和亚历山大多项式，被构造为量子不变量，即从量子群的表示和克尼日尼克-扎莫洛奇科夫方程解的单值性导出的不变量。随着Kontsevich不变量和Vassiliev不变量理论的引入，量子不变量变得组织良好。讨论了三维流形的量子不变量、微扰不变量、LMO不变量和有限型不变量。描述了Chern-Simons场论和Wess-Zumino-维滕模型作为不变量的物理背景。
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, ie 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.