Galois Theory, Coverings, and Riemann Surfaces
Askold Khovanskii, "Galois Theory, Coverings, and Riemann Surfaces"
English | ISBN: 364238840X | 2013 | 79 pages | PDF | 3 MB
English | ISBN: 364238840X | 2013 | 79 pages | PDF | 3 MB
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.