Galois theory, coverings, and Riemann surfaces
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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.
Nákup knihy
Galois theory, coverings, and Riemann surfaces, Askolʹd G. Chovanskij
- Jazyk
- Rok vydání
- 2013
Doručení
Platební metody
2021 2022 2023
Navrhnout úpravu
- Titul
- Galois theory, coverings, and Riemann surfaces
- Jazyk
- anglicky
- Autoři
- Askolʹd G. Chovanskij
- Vydavatel
- Springer
- Rok vydání
- 2013
- Vazba
- pevná
- ISBN10
- 364238840X
- ISBN13
- 9783642388408
- Kategorie
- Matematika
- Anotace
- 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.