Galois Theory, Coverings, and Riemann Surfaces

1. Front Matter

   Pages I-VIII

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2. Galois Theory

   • Askold Khovanskii

   Pages 1-40

3. Coverings

   • Askold Khovanskii

   Pages 41-63

4. Ramified Coverings and Galois Theory

   • Askold Khovanskii

   Pages 65-77

5. Back Matter

   Pages 79-81

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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.

• Galois group
• monodromy group
• solvability by radicals

From the reviews:

“This book features generalizations and variations beyond Abel’s theorem per se. … This book is for those who appreciate concision, and remarkably, the author develops these extended results in full detail--all in a work just a fraction of the length of standard Galois theory textbooks. Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 51 (10), June, 2014)

• Dept. Mathematics, University of Toronto, Toronto, Canada

  Askold Khovanskii

Askold Khovanskii is a Professor of Mathematics at the University of Toronto, and a principal researcher at the RAS Institute for Systems Analysis (Moscow, Russia). He is a founder of Topological Galois Theory and the author of fundamental results in this area.

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