阿贝尔链不变量与同调
Abelian link invariants and homology
摘要：
本文研究了具有紧规范群U（1）的量子Chern-Simons场论在封闭定向三维流形M中定义的链不变量。讨论了交换环不变量与环补的同调群的关系。我们证明，当M是一个同调球面，或者当一般流形M中的一个环是同调平凡的时，相关的观测量与球面S ^[3]的观测量重合。最后证明了流形M的U（1）Reshetikhin-Turaev手术不变量不仅是同调群的函数，也不仅是同伦型的函数.
英文摘要：
We consider the link invariants defined by the quantum Chern-Simons field theory with compact gauge group U(1) in a closed oriented 3-manifold M. The relation of the abelian link invariants with the homology group of the complement of the links is discussed. We prove that, when M is a homology sphere or when a link -in a generic manifold M- is homologically trivial, the associated observables coincide with the observables of the sphere S^3. Finally we show that the U(1) Reshetikhin-Turaev surgery invariant of the manifold M is not a function of the homology group only, nor a function of the homotopy type of M alone.
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