论文标题
二维CW-复合物的主要捆绑包，结构组断开
Principal bundles on 2-dimensional CW-complexes with disconnected structure group
论文作者
论文摘要
鉴于任何拓扑组$ g $，在有限的CW-Complex $ x $上对本金$ g $捆绑的拓扑分类是由一组免费的同型映射类别从$ x $到相应的分类空间$ bg $给出的。这种经典的结果已被长期使用，以根据明确的特征类提供这种分类。但是，即使$ x $的尺寸$ 2 $，似乎也没有明确考虑这种明确的分类。 $ g $是一个谎言组，其组件在其基本组$π_1g$上进行非凡起作用。在本说明中，我们通过在特征类方面获得分类来处理这种情况，而在有限的CW-COMPLEX $ 2 $的情况下，$ g $捆绑包$ 2 $，$ g $是一个谎言组，以至于$π_0g$是Abelian。
Given any topological group $G$, the topological classification of principal $G$-bundles over a finite CW-complex $X$ is long-known to be given by the set of free homotopy classes of maps from $X$ to the corresponding classifying space $BG$. This classical result has been long-used to provide such classification in terms of explicit characteristic classes. However, even when $X$ has dimension $2$, it seems there is a case in which such explicit classification has not been explicitly considered. This is the case where $G$ is a Lie group, whose group of components acts non-trivially on its fundamental group $π_1G$. In this note we deal with this case by obtaining the classification, in terms of characteristic classes, of principal $G$-bundles over a finite CW-complex of dimension $2$, with $G$ is a Lie group such that $π_0G$ is abelian.
