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 ...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.展开更多
文摘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.
