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.
ISBN: | 9783662519561 |
Publication date: | 23rd August 2016 |
Author: | Askold Khovanskii |
Publisher: | Springer an imprint of Springer Berlin Heidelberg |
Format: | Paperback |
Pagination: | 81 pages |
Genres: |
Algebra Algebraic geometry Topology Groups and group theory |