Topological Galois Theory

Author : Askold Khovanskii
Publisher : Springer
Page : 317 pages
File Size : 54,8 Mb
Release : 2014-10-10
Category : Mathematics
ISBN : 9783642388712

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Topological Galois Theory by Askold Khovanskii Pdf

This book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equations in explicit form. In particular, it offers a complete exposition of the relatively new area of topological Galois theory, initiated by the author. Applications of Galois theory to solvability of algebraic equations by radicals, basics of Picard–Vessiot theory, and Liouville's results on the class of functions representable by quadratures are also discussed. A unique feature of this book is that recent results are presented in the same elementary manner as classical Galois theory, which will make the book useful and interesting to readers with varied backgrounds in mathematics, from undergraduate students to researchers. In this English-language edition, extra material has been added (Appendices A–D), the last two of which were written jointly with Yura Burda.

Author : Askold Khovanskii
Publisher : Springer Science & Business Media
Page : 86 pages
File Size : 46,8 Mb
Release : 2013-09-11
Category : Mathematics
ISBN : 9783642388415

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Galois Theory, Coverings, and Riemann Surfaces by Askold Khovanskii Pdf

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.

Author : Francis Borceux,George Janelidze
Publisher : Cambridge University Press
Page : 360 pages
File Size : 52,8 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521803098

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Galois Theories by Francis Borceux,George Janelidze Pdf

Develops Galois theory in a more general context, emphasizing category theory.

Author : Victor P. Snaith
Publisher : Courier Corporation
Page : 322 pages
File Size : 44,8 Mb
Release : 2014-01-15
Category : Mathematics
ISBN : 9780486493589

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Topological Methods in Galois Representation Theory by Victor P. Snaith Pdf

"An advanced monograph on Galois representation theory by one of the world's leading algebraists, this volume is directed at mathematics students who have completed a graduate course in introductory algebraic topology. Topics include Abelian and nonabelian cohomology of groups, characteristic classes of forms and algebras, explicit Brauer induction theory, and much more. 1989 edition"--

Author : Tamás Szamuely
Publisher : Cambridge University Press
Page : 281 pages
File Size : 49,6 Mb
Release : 2009-07-16
Category : Mathematics
ISBN : 9780521888509

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Galois Groups and Fundamental Groups by Tamás Szamuely Pdf

Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.

Author : Jean-Pierre Serre
Publisher : CRC Press
Page : 120 pages
File Size : 42,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781439865255

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Topics in Galois Theory by Jean-Pierre Serre Pdf

This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt constructi

Author : Askold Khovanskii
Publisher : Unknown
Page : 92 pages
File Size : 43,6 Mb
Release : 2013-09-30
Category : Electronic
ISBN : 3642388426

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Galois Theory, Coverings, and Riemann Surfaces by Askold Khovanskii Pdf

Author : Dennis P. Sullivan
Publisher : Springer
Page : 286 pages
File Size : 42,8 Mb
Release : 2009-09-03
Category : Mathematics
ISBN : 9048103509

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Geometric Topology: Localization, Periodicity and Galois Symmetry by Dennis P. Sullivan Pdf

The seminal ‘MIT notes’ of Dennis Sullivan were issued in June 1970 and were widely circulated at the time. The notes had a - jor in?uence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including p-local, pro?nite and rational homotopy theory, le- ing to the solution of the Adams conjecture on the relationship between vector bundles and spherical ?brations, the formulation of the ‘Sullivan conjecture’ on the contractibility of the space of maps from the classifying space of a ?nite group to a ?nite dimensional CW complex, theactionoftheGalois groupoverQofthealgebraicclosureQof Q on smooth manifold structures in pro?nite homotopy theory, the K-theory orientation ofPL manifolds and bundles. Some of this material has been already published by Sullivan him- 1 self: in an article in the Proceedings of the 1970 Nice ICM, and in the 1974 Annals of Mathematics papers Genetics of homotopy theory and the Adams conjecture and The transversality character- 2 istic class and linking cycles in surgery theory . Many of the ideas originating in the notes have been the starting point of subsequent 1 reprinted at the end of this volume 2 joint with John Morgan vii viii 3 developments . However, the text itself retains a unique ?avour of its time, and of the range of Sullivan’s ideas.

Author : Rajnikant Sinha
Publisher : Springer Nature
Page : 351 pages
File Size : 40,9 Mb
Release : 2019-12-28
Category : Mathematics
ISBN : 9789811398490

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Galois Theory and Advanced Linear Algebra by Rajnikant Sinha Pdf

This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley–Hamilton theorem, Galois groups, Sylvester’s law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial.

Author : Grégory Berhuy
Publisher : Cambridge University Press
Page : 328 pages
File Size : 48,7 Mb
Release : 2010-09-09
Category : Mathematics
ISBN : 9781139490887

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An Introduction to Galois Cohomology and its Applications by Grégory Berhuy Pdf

This is the first detailed elementary introduction to Galois cohomology and its applications. The introductory section is self-contained and provides the basic results of the theory. Assuming only a minimal background in algebra, the main purpose of this book is to prepare graduate students and researchers for more advanced study.

Author : Ian Stewart
Publisher : Unknown
Page : 0 pages
File Size : 43,8 Mb
Release : 2021
Category : Galois theory
ISBN : 7560396437

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Galois Theory (Fourth Edition) by Ian Stewart Pdf

Author : Helmut Koch
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 50,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662049679

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Galois Theory of p-Extensions by Helmut Koch Pdf

Helmut Koch's classic is now available in English. Competently translated by Franz Lemmermeyer, it introduces the theory of pro-p groups and their cohomology. The book contains a postscript on the recent development of the field written by H. Koch and F. Lemmermeyer, along with many additional recent references.

Author : Frank Neumann,Sibylle Schroll
Publisher : Springer Nature
Page : 240 pages
File Size : 54,6 Mb
Release : 2020-09-26
Category : Mathematics
ISBN : 9783030517953

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Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants by Frank Neumann,Sibylle Schroll Pdf

This book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmüller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018. Within the theme of the workshop, the collected articles cover a broad range of topics and explore exciting new links between algebraic geometry, representation theory, group theory, number theory and algebraic topology. The book combines research and overview articles by prominent international researchers and provides a valuable resource for researchers and students alike.

Author : Gunter Malle,B. Heinrich Matzat
Publisher : Springer
Page : 533 pages
File Size : 53,6 Mb
Release : 2018-07-27
Category : Mathematics
ISBN : 9783662554203

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Inverse Galois Theory by Gunter Malle,B. Heinrich Matzat Pdf

A consistent and near complete survey of the important progress made in the field over the last few years, with the main emphasis on the rigidity method and its applications. Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a collection of the existing Galois realizations.

Author : Leila Schneps
Publisher : Cambridge University Press
Page : 384 pages
File Size : 54,6 Mb
Release : 1994-07-28
Category : Mathematics
ISBN : 0521478219

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The Grothendieck Theory of Dessins D'Enfants by Leila Schneps Pdf

Dessins d'Enfants are combinatorial objects, namely drawings with vertices and edges on topological surfaces. Their interest lies in their relation with the set of algebraic curves defined over the closure of the rationals, and the corresponding action of the absolute Galois group on them. The study of this group via such realted combinatorial methods as its action on the Dessins and on certain fundamental groups of moduli spaces was initiated by Alexander Grothendieck in his unpublished Esquisse d'un Programme, and developed by many of the mathematicians who have contributed to this volume. The various articles here unite all of the basics of the subject as well as the most recent advances. Researchers in number theory, algebraic geometry or related areas of group theory will find much of interest in this book.