论文标题
关于奇异流形的角色品种
On character varieties of singular manifolds
论文作者
论文摘要
在本文中，我们构建了一种松弛的单拓扑量子场理论，该理论在代数品种的Grothendieck环中计算虚拟类别的$ g $ - 代表品种而不是具有圆锥形奇异性的歧管，我们将调用NodeFolds。该构建对于任何维度和抛物线环境中的任何代数组$ g $都是有效的。特别是，这种TQFT使我们能够在复杂的单数平面曲线上计算虚拟类别的代表性类别。此外，如果$ g = \ mathrm {sl} _ {2}（k）$，则在非促谁和抛物线场景中计算相关字符的虚拟类别的虚拟类别。
In this paper, we construct a lax monoidal Topological Quantum Field Theory that computes virtual classes, in the Grothendieck ring of algebraic varieties, of $G$-representation varieties over manifolds with conic singularities, which we will call nodefolds. This construction is valid for any algebraic group $G$, in any dimension and also in the parabolic setting. In particular, this TQFT allow us to compute the virtual classes of representation varieties over complex singular planar curves. In addition, in the case $G = \mathrm{SL}_{2}(k)$, the virtual class of the associated character variety over a nodal closed orientable surface is computed both in the non-parabolic and in the parabolic scenarios.
