Topological Galois Theory Solvability and Unsolvability of Equations in Finite Terms /

• Main Author: Khovanskii, Askold (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Algebra.; Field theory (Physics).; Group theory.; Topological groups.; Lie groups.; Functions of complex variables.; Topology.; Field Theory and Polynomials.; Functions of a Complex Variable.; Group Theory and Generalizations.; Topological Groups, Lie Groups.; Several Complex Variables and Analytic Spaces.

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. A...

Table of Contents:

• Preface
• 1 Construction of Liouvillian Classes of Functions and Liouville’s Theory
• 2 Solvability of Algebraic Equations by Radicals and Galois Theory
• 3 Solvability and Picard–Vessiot Theory
• 4 Coverings and Galois Theory
• 5 One-Dimensional Topological Galois Theory
• 6 Solvability of Fuchsian Equations
• 7 Multidimensional Topological Galois Theory
• Appendix A: Straightedge and Compass Constructions
• Appendix B: Chebyshev Polynomials and Their Inverses
• Appendix C: Signatures of Branched Coverings and Solvability in Quadratures
• Appendix D: On an Algebraic Version of Hilbert’s 13th Problem
• References.