Topological Galois Theory [[electronic resource] ] : Solvability and Unsolvability of Equations in Finite Terms / / by Askold Khovanskii

• Autore: Khovanskii Askold
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2014
• Edizione: 1st ed. 2014.
• Descrizione fisica: 1 online resource (317 p.)
• Disciplina: 511.5
• Soggetto topico: Algebra; Field theory (Physics); Functions of complex variables; Group theory; Topological groups; Lie groups; Topology; Field Theory and Polynomials; Functions of a Complex Variable; Group Theory and Generalizations; Topological Groups, Lie Groups; Several Complex Variables and Analytic Spaces
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Topological Galois Theory
• ISBN: 3-642-38871-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910299983503321
• Lo trovi qui: Univ. Federico II
• Serie: Springer Monographs in Mathematics, . 1439-7382