论文标题
图形的配置空间中的删除和收缩
Deletion and contraction in configuration spaces of graphs
论文作者
论文摘要
本文的目的是提供图形的配置空间之间的空间水平图，这些图形由代数操纵细胞链预测。更明确地，我们考虑边缘收缩和半边的删除，并根据简单图的配置空间来识别同型辅助机。构建的主要好处在于使操作功能功能 - 尤其是图形未成年人在基本组以及广义（CO）同源理论的层面上产生兼容地图。 作为应用，我们在任何广义的共同体学理论中为半边的缺失提供了一个长的精确序列，与诸如Steenrod和Adams操作之类的同种学操作兼容，允许在这种一般环境中进行归纳计算。我们还表明，无序配置空间的广义同源性被有限地生成，作为对面的次要类别的表示形式。
The aim of this article is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and identify the homotopy cofibers in terms of configuration spaces of simpler graphs. The construction's main benefit lies in making the operations functorial - in particular, graph minors give rise to compatible maps at the level of fundamental groups as well as generalized (co)homology theories. As applications we provide a long exact sequence for half-edge deletion in any generalized cohomology theory, compatible with cohomology operations such as the Steenrod and Adams operations, allowing for inductive calculations in this general context. We also show that the generalized homology of unordered configuration spaces is finitely generated as a representation of the opposite graph minor category.
