论文标题
在单数$（g，x）$ - 歧管的分支封面上
On branched coverings of singular $(G,X)$-manifolds
论文作者
论文摘要
分支覆盖物的历史悠久，从对黎曼表面的冲突到实现3个manifolds，因为覆盖了一个结上的分支；从几何拓扑到代数几何学。本工作调查了覆盖“ fox”的分支的概念，这对于（g，x） - manifolds尤其自然。工作是两个折。首先，我们回想起并丰富了当前的艺术状态（基于蒙特西诺斯），并为这种分支覆盖的Galois理论以及对纤维上方的纤维的描述进行了描述。结果，我们解决了蒙特西诺斯的两个开放问题，并构建了一个与另一个开放问题有关的示例。其次，我们提出了一个单数（g，x） - manifolds的理论，并应用了我们开发的分支覆盖的理论，以将（g，x） - manifolds的通常框架扩展到单数（g，x）-manifolds；特别是，我们为这种奇异流形构建了一个开发图。给出了奇异的局部Minkowski歧管的应用。
Branched covering have a long history from ramification of Riemann surfaces to realization of 3-manifolds as covering ramified over a knots; from geometrical topology to algebraic geometry. The present work investigates a notion of branched covering "à la Fox" which is particularly natural for (G,X)-manifolds. The work is two fold. First, we recall and enrich the current state of the art (based upon Montesinos) and develop a Galois theory for such branched covering together with a description of the fiber above branching points. As a consequence, we solve two open questions of Montesinos and construct an example related to another open question. Second, we present a theory of singular (G,X)-manifolds and apply the theory of branched covering we developped to extend the usual framework of (G,X)-manifolds to singular (G,X)-manifolds; in particular, we construct a developping map for such singular manifolds. An application to singular locally Minkowski manifolds is given.
