Galois Theory, Coverings, and Riemann Surfaces
Nonfiction, Science & Nature, Mathematics, Topology, Algebra
| Author: | Askold Khovanskii | ISBN: | 9783642388415 |
| Publisher: | Springer Berlin Heidelberg | Publication: | September 11, 2013 |
| Imprint: | Springer | Language: | English |
| Author: | Askold Khovanskii |
| ISBN: | 9783642388415 |
| Publisher: | Springer Berlin Heidelberg |
| Publication: | September 11, 2013 |
| Imprint: | Springer |
| Language: | English |
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.
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.
