论文标题
在表面的表示形式的卷胶配方中
Gluing Formulas for Volume Forms on Representation Varieties of Surfaces
论文作者
论文摘要
令$σ_{g，n} $是一个紧凑的面向表面，属$ g \ geq 2 $由$ n $圆圈边界。由于Witten，扭曲的reidemister扭转与Atiyah-Bott-Goldman-Narasimhan narasimhan symbletectic形式的力量相吻合，在$π_1（σ_{g，0}）$的代表空间中，在任何半简单的Lie lie Group中。在本文中，我们首先获得了$σ_{g，0} $的扭曲式粘合公式，以$σ_{2,2}，$ $ $ $σ_{2,1}，$和边界圆圈$ \ nathbb {s}^1. $ portious的$σ_{2,2}，$ $ $σ_{2,1}。我们表明，$σ_{g，0} $在表示形式上的符号卷形式可以表示为圆形符号体积卷的产物，上面的相对表示形式$σ_{2,1} $和$σ_{2,2}。
Let $Σ_{g,n}$ be a compact oriented surface with genus $g\geq 2$ bordered by $n$ circles. Due to Witten, the twisted Reidemeister torsion coincides with a power of the Atiyah-Bott-Goldman-Narasimhan symplectic form on the space of representations of $π_1(Σ_{g,0})$ in any semi-simple Lie group. In the present paper, we first obtain a multiplicative gluing formula for the twisted Reidemeister torsion of $Σ_{g,0}$ in terms of torsions of $Σ_{2,2},$ $Σ_{2,1},$ and boundary circles $\mathbb{S}^1.$ Then, by using Heusener and Porti's results on $Σ_{g,n},$ we show that the symplectic volume form on the representation variety of $Σ_{g,0}$ can be expressed as a product of the holomorphic symplectic volume forms on the relative representation varieties of surfaces $Σ_{2,1}$ and $Σ_{2,2}.$
