Semi-topological Galois Theory

Hsuan-Yi Liao, Jyh-Haur Teh
2015 Algebra Colloquium  
We introduce splitting coverings to enhance the well known analogy between field extensions and covering spaces. Semi-topological Galois groups are defined for Weierstrass 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. 2000 Mathematics Subject Classification. Primary 13B05, 55R10; Secondary 12F12.
doi:10.1142/s1005386715000589 fatcat:yszsl6kdlra2fe3elwwkgsv3sy