Semi-topological Galois Theory

• 作者: Hsuan-Yi Liao Jyh-Haur Teh
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 伽罗瓦理论 半拓扑 伽罗瓦群 应用程序 多项式 覆盖 分裂 辫群
• 年，卷（期）: 2015,（4）
• 页码范围: 687-706
• 页数: 20页
• 分类号: O152
• 语种: 中文

摘要

We introduce splitting coverings to enhance the well known analogy between field extensions and covering spaces. Semi-topological Galois groups are defined for Weier- strass polynomials and a Galois correspondence is proved. Combining results from braid groups, we solve the topological inverse Galois problem. As an application, symmetric and cyclic groups are realized over Q.