Topological Galois Theory

Solvability and Unsolvability of Equations in Finite Terms

  • Askold Khovanskii

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Askold Khovanskii
    Pages 85-106
  3. Askold Khovanskii
    Pages 107-141
  4. Askold Khovanskii
    Pages 143-171
  5. Askold Khovanskii
    Pages 173-193
  6. Askold Khovanskii
    Pages 195-238
  7. Back Matter
    Pages 239-307

About this book


This book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equations in explicit form. In particular, it offers a complete exposition of the relatively new area of topological Galois theory, initiated by the author. Applications of Galois theory to solvability of algebraic equations by radicals, basics of Picard–Vessiot theory, and Liouville's results on the class of functions representable by quadratures are also discussed.

A unique feature of this book is that recent results are presented in the same elementary manner as classical Galois theory, which will make the book useful and interesting to readers with varied backgrounds in mathematics, from undergraduate students to researchers.

In this English-language edition, extra material has been added (Appendices A–D), the last two of which were written jointly with Yura Burda.


Galois group Monodromy group Solvability by quadratures Solvability by radicals

Authors and affiliations

  • Askold Khovanskii
    • 1
  1. 1.University of Toronto, Department of MathematicsTorontoCanada

Bibliographic information