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Topological Galois theory: solvability and unsolvability of equations in finite terms

Topological Galois theory: solvability and unsolvability of equations in finite terms
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Dewey Class 514 (DDC 23.)
Title Topological Galois theory (M) : solvability and unsolvability of equations in finite terms / Askold Khovanskii
Author Khovanskii, Askold Georgievič
Publication Heidelberg : Springer , 2014
Physical Details ix, 307 pages ; 24 cm
Series Springer monographs in mathematics
ISBN 9783642388705
Summary Note 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.:
Contents note 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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