Galois Theory, Coverings, and Riemann Surfaces

Authors: Khovanskii, Askold

  • Classical Galois theory and classification of coverings are explained from scratch
  • Gentle introduction to the cutting edge of research
  • Written by one of the founders of topological Galois theory
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About this Textbook

The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to the topological Galois theory developed by the author.

All results are presented in the same elementary and self-contained manner as classical Galois theory, making this book both useful and interesting to readers with a variety of backgrounds in mathematics, from advanced undergraduate students to researchers.

About the authors

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.

Reviews

From the reviews:

“This book features generalizations and variations beyond Abel’s theorem per se. … This book is for those who appreciate concision, and remarkably, the author develops these extended results in full detail--all in a work just a fraction of the length of standard Galois theory textbooks. Summing Up: Recommended. Upper-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 51 (10), June, 2014)

Table of contents (3 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-642-38841-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $49.99
price for USA
  • ISBN 978-3-642-38840-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $49.99
price for USA
  • ISBN 978-3-662-51956-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Galois Theory, Coverings, and Riemann Surfaces
Authors
Translated by
Timorin, V., Kiritchenko, V.
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-38841-5
DOI
10.1007/978-3-642-38841-5
Hardcover ISBN
978-3-642-38840-8
Softcover ISBN
978-3-662-51956-1
Edition Number
1
Number of Pages
VIII, 81
Topics