论文标题
团体组合及其在捆绑理论中的应用
Frames of group-sets and their application in bundle theory
论文作者
论文摘要
我们研究纤维束，其中纤维不是集团的$ g $，而是带有脱节轨道的免费$ g $空间。这些捆绑包非常类似于校长捆绑包，因此我们称它们为半主体捆绑包。通过类似于矢量空间的基础来定义$ g $ set的基础的概念，可以促进对此类捆绑包的研究。这些基地的对称组是花圈产品。与矢量束相似，使用基础概念诱导框架束结构，在这种情况下，这会导致用花圈产品作为结构组的主要束。该结构可以用函子的语言进行形式化，该语言将半主体束缩回主要捆绑包。此外，半原则捆绑包一样支持平行运输，就像主要捆绑包一样，这将转移到框架束上。
We study fiber bundles where the fibers are not a group $G$, but a free $G$-space with disjoint orbits. These bundles closely resemble principal bundles, hence we call them semi-principal bundles. The study of such bundles is facilitated by defining the notion of a basis of a $G$-set, in analogy with a basis of a vector space. The symmetry group of these bases is a wreath product. Similar to vector bundles, using the notion of a basis induces a frame bundle construction, which in this case results in a principal bundle with the wreath product as structure group. This construction can be formalized in the language of a functor, which retracts the semi-principal bundles to the principal bundles. In addition, semi-principal bundles support parallel transport just like principal bundles, and this carries over to the frame bundle.
