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Mathematics - Algebra | Galois Theory, Coverings, and Riemann Surfaces

Galois Theory, Coverings, and Riemann Surfaces

Khovanskii, Askold

Translated by Timorin, V., Kiritchenko, V.

2013, VIII, 81 p.

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  • 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

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.

Content Level » Graduate

Keywords » Galois group - monodromy group - solvability by radicals

Related subjects » Algebra - Geometry & Topology

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