Topological Galois Theory

Solvability and Unsolvability of Equations in Finite Terms

AvAskold Khovanskii

Häftad, Engelska, 2016

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2016-08-23
Mått:155 x 235 x 18 mm
Vikt:499 g
Format:Häftad
Språk:Engelska
Serie:Springer Monographs in Mathematics
Antal sidor:307
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783662506028
Originaltitel:Topologicheskaya Teoriya Galua
Översättare:Vladlen Timorin, Valentina Kiritchenko, Liudmyla Kadets

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Grupper och gruppteori inom Naturvetenskap och teknik
Algebra inom Naturvetenskap och teknik

Mer om författaren

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.

Recensioner i media

"This book offers the possibility to learn about the very interesting topological Galois theory, as well as to parallel it with the algebraic and differential Galois theories. It is very well-written and self-contained, making its reading really enjoyable." (Teresa Crespo, zbMATH 1331.12001, 2016)

Innehållsförteckning

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.