Overview
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
Includes supplementary material: sn.pub/extras
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Table of contents (3 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
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)Authors and Affiliations
About the author
Bibliographic Information
Book Title: Galois Theory, Coverings, and Riemann Surfaces
Authors: Askold Khovanskii
DOI: https://doi.org/10.1007/978-3-642-38841-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2013
Hardcover ISBN: 978-3-642-38840-8Published: 20 November 2013
Softcover ISBN: 978-3-662-51956-1Published: 23 August 2016
eBook ISBN: 978-3-642-38841-5Published: 11 September 2013
Edition Number: 1
Number of Pages: VIII, 81
Topics: Field Theory and Polynomials, Group Theory and Generalizations, Topology, Algebra, Algebraic Geometry