论文标题
等级的代表品种
Representation variety for the rank one affine group
论文作者
论文摘要
本文的目的是研究表面组的虚拟类别的虚拟类别，以列为等级的一个仿射组。我们通过三种不同的方法执行此计算：几何方法，基于将表示变体分为较简单的部分；算术方法的重点是计算其在有限场上的点数；和量子方法，该方法通过拓扑量子场理论执行计算。我们还讨论了表示形式和性格品种的相应模量空间，由于基础群体的非还原性，事实证明这是不等式的。
The aim of this paper is to study the virtual classes of representation varieties of surface groups onto the rank one affine group. We perform this calculation by three different approaches: the geometric method, based on stratifying the representation variety into simpler pieces; the arithmetic method, focused on counting their number of points over finite fields; and the quantum method, which performs the computation by means of a Topological Quantum Field Theory. We also discuss the corresponding moduli spaces of representations and character varieties, which turn out to be non-equivalent due to the non-reductiveness of the underlying group.
