Topological Galois Theory Solvability and Unsolvability of Equations
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 topologi
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Askold Khovanskii
Topological Galois Theory Solvability and Unsolvability of Equations in Finite Terms
Springer Monographs in Mathematics
More information about this series at http://www.springer.com/series/3733
Askold Khovanskii
Topological Galois Theory Solvability and Unsolvability of Equations in Finite Terms
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Askold Khovanskii Department of Mathematics University of Toronto Toronto, Ontario Canada Translators: V. Timorin and V. Kirichenko: Chapters 1–7. Lucy Kadets: Appendices A and B. Appendices C and D were written jointly with Yura Burda. Based on Russian edition entitled “Topologicheskaya Teoriya Galua, Razreshimost i nerazreshimost uravnenii v konechnom vide”, published by MCCME, Moscow, Russia, 2008.
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-3-642-38870-5 ISBN 978-3-642-38871-2 (eBook) DOI 10.1007/978-3-642-38871-2 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2014952224 Mathematics Subject Classification (2010): 55-02, 34M15, 32Q55, 12F10, 30F10 © Springer-Verlag Berlin Heidelberg 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To the memory of Vladimir Igorevich Arnold
Preface
Numerous unsuccessful attempts to solve certain algebraic and differentia
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