{chamber Systems, Coloured Graphs and Orbifolds
{chamber Systems, Coloured Graphs and Orbifolds
复制标题
{腔室系统、彩色图表和 Orbifolds
DOI：
--
复制
发表时间：
1996
期刊：
影响因子：
--
通讯作者：
A. Valverde
中科院分区：
文献类型：
--
作者：
L. Balke;A. Valverde
我们用纯代数术语定义了房间系统的覆盖投影的概念，并为这种覆盖的甲板变换组构造了一个表示。将这个概念翻译成轨道折叠的语言就可以得到轨道折叠基本群的表示。在文献中，人们可以找到至少两种不同的方法来解决通过某种组合结构以有效方式编码流形的问题。一种方法使用彩色图表（作为参考，参见例如 5]）。另一种方法采用{腔室系统（参见4）。后一个概念是由 Dress 开发的，作为一种描述简单连通流形的平铺的方法，该流形相对于作用于该流形的某个群是等变的。他所谓的德莱尼符号与这种等变平铺相关联，包含有关轨道折叠的完整信息，这是通过传递到群作用的轨道空间而获得的。在彩色图的语言中，还存在编码 orbifold{ 结构的概念：覆盖物或折叠覆盖物的概念（参见 2]）。
We deene the notion of covering projections for {chamber systems in purely algebraic terms and construct a presentation for the group of decktransfor-mations of such a covering. Translating this concept into the language of orbifolds yields a presentation of the fundamental group of an orbifold. In the literature, one can nd at least two diierent approaches to the problem of encoding manifolds in an eecient way, by means of some combinatorial structure. One method uses coloured graphs (as reference see e.g. 5]). The other approach employs {chamber systems (cf. 4]). The latter concept was developed by Dress, as a method of describing tilings of a simply connected manifold which are equivariant with respect to some group, acting on that manifold. His so{called Delaney symbol, which is associated with such an equivariant tiling, contains the complete information about the orbifold which one obtains by passing to the orbit space of the group action. In the language of coloured graphs, there also exists a notion for encoding orbifold{ structures: the concept of coverings, or folded coverings (cf. 2]).