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)
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