Galois Theory, Coverings, and Riemann Surfaces

Khovanskii, Askold; Timorin, Vladlen; Kiritchenko, Valentina

The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the 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 the topological Galois theory developed by the author.

All results are presented in the same elementary and self-contained manner as classical Galois theory, making this book both useful and interesting to readers with a variety of backgrounds in mathematics, from advanced undergraduate students to researchers.

Details

Published by: Springer

Publication Date: 2016-08-23

Format: Paperback

ISBN-13: 9783662519561

DOI: 10.1007/978-3-642-38841-5

Dimensions: 235cm x155cm

Pages: 81