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

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

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...

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Bibliographic Details
Published in:Springer eBooks
Main Author: Khovanskii, Askold (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014.
Series:Springer Monographs in Mathematics,
Subjects:
mathematics.
Field theory (Physics).
Group theory.
Topological Groups.
Functions of complex variables.
Differential equations, partial.
Topology.
Mathematics.
Field Theory and Polynomials.
Functions of a Complex Variable.
Group Theory and Generalizations.
Topological Groups, Lie Groups.
Several Complex Variables and Analytic Spaces.
Online Access:http://dx.doi.org/10.1007/978-3-642-38871-2
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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.

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