论文标题
全球表面单学的衍生物用于非亚伯式的Gerbe
The derivative of global surface-holonomy for a non-abelian gerbe
论文作者
论文摘要
从以非亚伯差分差异共生表示的非亚伯式GERBE开始，在给定的交叉模块中的值，本文明确计算了映射到碱基流形的正方形的相关表面自由度的衍生物的公式；后来被视为特殊情况。虽然本文用于Gerbes的定义，但它们的连接和诱导的固体最初将是简单的，但在基于显式坐标的计算中，将向助手提供转换为立方体设置。尽管有许多先前发表的有关这些非亚洲gerbes的特性的结果，包括对单个开放式集合的衍生物的一些计算，但本文努力将这些局部计算进行处理，并在多个开放式集合中将它们粘合在一起，以便获得单个表达式，以使表达式变化，以与一个单品群的Squares家族有关。
Starting with a non-abelian gerbe represented by a non-abelian differential cocycle, with values in a given crossed-module, this paper explicitly calculates a formula for the derivative of the associated surface holonomy of squares mapped into the base manifold; with spheres later considered as a special case. While the definitions in this paper used for gerbes, their connections, and the induced holonomy will initially be simplicial, translations into a cubical setting will be provided to aide in explicit coordinate-based calculations. While there are many previously published results on the properties of these non-abelian gerbes, including some calculations of the derivative over a single open set, this paper endeavors to take these local calculations and glue them together across multiple open sets in order to obtain a single expression for the change in surface holonomy with respect to a one-parameter family of squares.
