论文标题
表面德林菲尔德扭矩I：较高属的副人
Surface Drinfeld Torsors I : Higher Genus Associators
论文作者
论文摘要
我们借着Operad理论开发了较高的Drinfeld伙伴属。我们首先引入一个构架版本的理性协会和Grothendieck-Teichmüller组，并证明其定义与框架数据无关。接下来，我们定义了通用KZ连接的框架版本，并使用它来表明，在复数上，理性框架的德林菲尔德·托索尔（Drinfeld Torsor）并不为空。接下来，我们专注于这个故事的较高属版本。我们定义了一个构造括号内的括号内质子辫子的大属属模块，并定义了其和弦图对应物。然后，我们使用这些操作模块来操作定义较高的属副群和Grothendieck-teichmüller组，这再次不依赖于框架数据。最后，我们将属于$ 1 $的案例中的结果与出现在垃圾中的结果进行了比较。
We develop a higher genus version of Drinfeld associators by means of operad theory. We start by introducing a framed version of rational associators and Grothendieck-Teichmüller groups and show that their definition is independent of the framing data. Next, we define a framed version of the universal KZ connection and we use it to show that over the complex numbers, the rational framed Drinfeld torsor is not empty. Next, we concentrate on the higher genus version of this story. We define an operad module of framed parenthesized higher genus braidings in prounipotent groupoids and we define its chord diagram counterpart. We then use these operadic modules to operadicly define higher genus associators and Grothendieck-Teichmüller groups, which again do not depend on the framing data. Finally, we compare our results in the genus $1$ case with those appearing in the litterature.
