Galois Theory, Coverings, and Riemann Surfaces

The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to the questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to topological Galois theory developed by the author. All results are presented in the same elementary and self-contained manner as classical Galois theory. Due to this feature, the book will be useful and interesting to readers with very different background in mathematics, from undergraduate students to researchers.

• ISBN: 978-3-642-38840-8
• Editorial: Springer
• Encuadernacion: Cartoné
• Fecha Publicación: 31/10/2013
• Nº Volúmenes: 1
• Idioma: Inglés