论文标题
迈向对四维点组的几何理解
Towards a Geometric Understanding of the 4-Dimensional Point Groups
论文作者
论文摘要
我们在4空间中对有限的正交转换组进行了分类，并使用极性轨道多面体从其几何作用的角度研究了这些组。对于一种类型的组（圆环组），我们根据它们对不变的圆环的行动进行了新的分类，而我们依靠其余组的经典结果。作为一种工具，我们开发了三个球体上定向的大圆圈的方便参数化，这以自然方式导致（定向）HOPF纤维。
We classify the finite groups of orthogonal transformations in 4-space, and we study these groups from the viewpoint of their geometric action, using polar orbit polytopes. For one type of groups (the toroidal groups), we develop a new classification based on their action on an invariant torus, while we rely on classic results for the remaining groups. As a tool, we develop a convenient parameterization of the oriented great circles on the 3-sphere, which leads to (oriented) Hopf fibrations in a natural way.
