纤维球3-orbifolds
Fibered spherical 3-orbifolds
摘要：
在20世纪30年代早期塞弗特和Threlfall分类共轭有限子群的$\mathrm{SO}(4)$，这给了代数分类定向球面3 orbifolds。在大多数情况下，球形3-orbifold是塞弗特纤维。Dunbar描述了非纤维球面3-orbifold的基础拓扑空间和奇异集。本文讨论了纤维情形，特别给出了$\mathrm{SO}(4)$的有限子群与相应的纤维3-orbifolds的不变量之间的显式关系。这允许直接从球面3-orbifolds的代数分类的拓扑性质推导。
英文摘要：
In early 1930s Seifert and Threlfall classified up to conjugacy the finite subgroups of $\mathrm{SO}(4)$, this gives an algebraic classification of orientable spherical 3-orbifolds. For the most part, spherical 3-orbifolds are Seifert fibered. The underlying topological space and singular set of non-fibered spherical 3-orbifolds were described by Dunbar. In this paper we deal with the fibered case and in particular we give explicit formulae relating the finite subgroups of $\mathrm{SO}(4)$ with the invariants of the corresponding fibered 3-orbifolds. This allows to deduce directly from the algebraic classification topological properties of spherical 3-orbifolds.
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