Galois Theory, Coverings, and Riemann Surf...

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

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: [...]

Inhaltsverzeichnis

Chapter 1 Galois Theory: 1.1 Action of a Solvable Group and Representability by Radicals.- 1.2 Fixed Points under an Action of a Finite Group and Its Subgroups.- 1.3 Field Automorphisms and Relations between Elements in a Field.- 1.4 Action of a k-Solvable Group and Representability by k-Radicals.- 1.5 Galois Equations.- 1.6 Automorphisms Connected with a Galois Equation.- 1.7 The Fundamental Theorem of Galois Theory.- 1.8 A Criterion for Solvability of Equations by Radicals.- 1.9 A Criterion for Solvability of Equations by k-Radicals.- 1.10 Unsolvability of Complicated Equations by Solving Simpler Equations.- 1.11 Finite Fields.- Chapter 2 Coverings: 2.1 Coverings over Topological Spaces.- 2.2 Completion of Finite Coverings over Punctured Riemann Surfaces.- Chapter 3 Ramified Coverings and Galois Theory: 3.1 Finite Ramified Coverings and Algebraic Extensions of Fields of Meromorphic Functions.- 3.2 Geometry of Galois Theory for Extensions of a Field of Meromorphic Functions.- References.- Index

Details

Erscheinungsjahr:	2013
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	viii 81 S.
ISBN-13:	9783642388408
ISBN-10:	364238840X
Sprache:	Englisch
Herstellernummer:	12804627
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Khovanskii, Askold
Übersetzung:	Kiritchenko, Valentina Timorin, Vladlen
Hersteller:	Springer Berlin Springer Berlin Heidelberg
Maße:	241 x 160 x 12 mm
Von/Mit:	Askold Khovanskii
Erscheinungsdatum:	20.11.2013
Gewicht:	0,319 kg

Artikel-ID: 105691502