Topological Galois theory : solvability and unsolvability of equations in finite terms / Askold Khovanskii.
Series: Springer monographs in mathematicsPublication details: Berlin : Springer-Verlag, 2014.Description: xviii, 307 p. ; 24 cmISBN:- 9783642388705
- 512.32 23 K45
Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
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Books | ISI Library, Kolkata | 512.32 K45 (Browse shelf(Opens below)) | Available | 136315 |
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512.32 F532 Interval orders and interval graphs : a study of partially ordered sets | 512.32 J37 Algebraic patching | 512.32 K45 Galois theory, coverings, and Riemann surfaces / | 512.32 K45 Topological Galois theory : | 512.32 N555 A classical introduction to Galois theory / | 512.32 Sch359 Galois representations and (Phi, Gamma)-modules / | 512.32 W244 Finite fields and Galois rings |
Includes bibliographical references and index.
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 Gaolis theory --
5. One-dimensional topological Galois theory --
6. Solvability of Fuchsian equations --
7. Multidimensional topological Galois theory --
A. Straightedge and compass constructions --
B. Chebyshev polynominals and their inverses --
C. Signatures of branched coverings and solvability in quadratures --
D. On an algebraic version of Hilbert's 13th problem--
References--
Index.
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.
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