论文标题
通过拓扑量子场理论量化代数不变性
Quantization of algebraic invariants through Topological Quantum Field Theories
论文作者
论文摘要
在本文中，我们研究了构建拓扑量子场理论（TQFTS）以量化代数不变性的问题。我们根据欧拉特征表现出必要的定量条件。在表面的情况下，还通过几乎tqfts和几乎是宽阔的代数为宽的TQFT提供了部分答案。作为一个应用程序，我们表明，$ g $代表品种的Poincaré多项式并不是任何代数$ g $的正数$ g $的单型tqfts。
In this paper we investigate the problem of constructing Topological Quantum Field Theories (TQFTs) to quantize algebraic invariants. We exhibit necessary conditions for quantizability based on Euler characteristics. In the case of surfaces, also provide a partial answer in terms of sufficient conditions by means of almost-TQFTs and almost-Frobenius algebras for wide TQFTs. As an application, we show that the Poincaré polynomial of $G$-representation varieties is not a quantizable invariant by means of a monoidal TQFTs for any algebraic group $G$ of positive dimension.
