论文标题
简单三维紧凑型谎言组的轨道空间的拓扑和同源性能
Topological and homological properties of the orbit space of a simple three-dimensional compact linear Lie group
论文作者
论文摘要
该文章致力于一个问题，即紧凑型线性群的轨道空间是否是拓扑歧管和同源歧管。在本文中，考虑了一个简单的三维组的情况。对于表示商空间是同源歧管的表示形式的不可还原组件的半径积分部分的总和，获得了上限，如果表示的商的商品是平滑的歧管，则可以增强较早的结果，从而产生相同的界限。以前还研究了满足该界限的大多数表示。在证据中，使用线性代数，谎言群和代数及其表示的标准论点。
The article is devoted to the question whether the orbit space of a compact linear group is a topological manifold and a homological manifold. In the paper, the case of a simple three-dimensional group is considered. An upper bound is obtained for the sum of the half-dimension integral parts of the irreducible components of a representation whose quotient space is a homological manifold, that enhances an earlier result giving the same bound if the quotient space of a representation is a smooth manifold. The most of the representations satisfying this bound are also researched before. In the proofs, standard arguments from linear algebra, theory of Lie groups and algebras and their representations are used.
