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Galois Theory, Coverings, and Riemann Surfaces

  • Askold Khovanskii

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Askold Khovanskii
    Pages 1-40
  3. Askold Khovanskii
    Pages 41-63
  4. Askold Khovanskii
    Pages 65-77
  5. Back Matter
    Pages 79-81

About this book

Introduction

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.

Keywords

Galois group monodromy group solvability by radicals

Authors and affiliations

  • Askold Khovanskii
    • 1
  1. 1.Dept. MathematicsUniversity of TorontoTorontoCanada

Bibliographic information