论文标题
增强架和表面丝带旋转不变的扩展
Extensions of Augmented Racks and Surface Ribbon Cocycle Invariants
论文作者
论文摘要
机架是一个具有直接不可及的二进制操作的集合，分别与Reidemeister Moves II和III相对应。如果操作是由小组操作编写的，则据说架子是{\ IT增强架子}。架子及其协同理论已被广泛用于结和打结的表面不变。与群体的共同体相似，架子2循环与扩展相关，并且出现的一个自然问题是表征增强架子本身是增强架子的增强架的扩展。在本文中，我们根据我们所谓的{\ fibrant and添加剂}的共同体来表征这种扩展。考虑了架子和组的同时扩展，其中相应的$ 2 $ cocycles通过某个公式相关。此外，我们为紧凑的定向表面构建着着色和旋转的不变性，并以嵌入$ 3 $ - 空格的色带形式为边界。
A rack is a set with a binary operation that is right-invertible and self-distributive, properties diagrammatically corresponding to Reidemeister moves II and III, respectively. A rack is said to be an {\it augmented rack} if the operation is written by a group action. Racks and their cohomology theories have been extensively used for knot and knotted surface invariants. Similarly to group cohomology, rack 2-cocycles relate to extensions, and a natural question that arises is to characterize the extensions of augmented racks that are themselves augmented racks. In this paper, we characterize such extensions in terms of what we call {\it fibrant and additive} cohomology of racks. Simultaneous extensions of racks and groups are considered, where the respective $2$-cocycles are related through a certain formula. Furthermore, we construct coloring and cocycle invariants for compact orientable surfaces with boundary in ribbon forms embedded in $3$-space.
