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Topological Galois Theory
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Book Synopsis Topological Galois Theory by : Askold Khovanskii
Download or read book Topological Galois Theory written by Askold Khovanskii and published by Springer. This book was released on 2014-10-10 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Galois Theory, Coverings, and Riemann Surfaces by : Askold Khovanskii
Download or read book Galois Theory, Coverings, and Riemann Surfaces written by Askold Khovanskii and published by Springer Science & Business Media. This book was released on 2013-09-11 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Galois Theories by : Francis Borceux
Download or read book Galois Theories written by Francis Borceux and published by Cambridge University Press. This book was released on 2001-02-22 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.
Book Synopsis Galois Groups and Fundamental Groups by : Tamás Szamuely
Download or read book Galois Groups and Fundamental Groups written by Tamás Szamuely and published by Cambridge University Press. This book was released on 2009-07-16 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Book Synopsis Topics in Galois Theory by : Jean-Pierre Serre
Download or read book Topics in Galois Theory written by Jean-Pierre Serre and published by CRC Press. This book was released on 2016-04-19 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Geometric Topology: Localization, Periodicity and Galois Symmetry by : Dennis P. Sullivan
Download or read book Geometric Topology: Localization, Periodicity and Galois Symmetry written by Dennis P. Sullivan and published by Springer. This book was released on 2009-09-03 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Profinite Groups, Arithmetic, and Geometry by : Stephen S. Shatz
Download or read book Profinite Groups, Arithmetic, and Geometry written by Stephen S. Shatz and published by Princeton University Press. This book was released on 2016-03-02 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a treatment of duality. His objective is to present effectively that body of material upon which all modern research in Diophantine geometry and higher arithmetic is based, and to do so in a manner that emphasizes the many interesting lines of inquiry leading from these foundations.
Book Synopsis An Extension of the Galois Theory of Grothendieck by : André Joyal
Download or read book An Extension of the Galois Theory of Grothendieck written by André Joyal and published by American Mathematical Soc.. This book was released on 1984 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we compare, in a precise way, the concept of Grothendieck topos to the classical notion of topological space. The comparison takes the form of a two-fold extension of the idea of space.
Book Synopsis Galois Theory (Fourth Edition) by : Ian Stewart
Download or read book Galois Theory (Fourth Edition) written by Ian Stewart and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Model Theory by : Jörg Flum
Download or read book Topological Model Theory written by Jörg Flum and published by Springer. This book was released on 2006-11-14 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Groups as Galois Groups by : Helmut Völklein
Download or read book Groups as Galois Groups written by Helmut Völklein and published by Cambridge University Press. This book was released on 1996-08-13 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops the mathematical background and recent results on the Inverse Galois Problem.
Book Synopsis Topological Methods in Hydrodynamics by : Vladimir I. Arnold
Download or read book Topological Methods in Hydrodynamics written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.
Download or read book Galois Theory written by Emil Artin and published by . This book was released on 2020-02 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author Emil Artin is known as one of the greatest mathematicians of the 20th century. He is regarded as a man who gave a modern outlook to Galois theory. Original lectures by the master. This emended edition is with completely new typesetting and corrections. The free PDF file available on the publisher's website www.bowwowpress.org
Book Synopsis Theories, Sites, Toposes by : Olivia Caramello
Download or read book Theories, Sites, Toposes written by Olivia Caramello and published by Oxford University Press. This book was released on 2018 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to Grothendieck, the notion of topos is "the bed or deep river where come to be married geometry and algebra, topology and arithmetic, mathematical logic and category theory, the world of the continuous and that of discontinuous or discrete structures". It is what he had "conceived of most broad to perceive with finesse, by the same language rich of geometric resonances, an "essence" which is common to situations most distant from each other, coming from one region or another of the vast universe of mathematical things". The aim of this book is to present a theory and a number of techniques which allow to give substance to Grothendieck's vision by building on the notion of classifying topos educed by categorical logicians. Mathematical theories (formalized within first-order logic) give rise to geometric objects called sites; the passage from sites to their associated toposes embodies the passage from the logical presentation of theories to their mathematical content, i.e. from syntax to semantics. The essential ambiguity given by the fact that any topos is associated in general with an infinite number of theories or different sites allows to study the relations between different theories, and hence the theories themselves, by using toposes as 'bridges' between these different presentations. The expression or calculation of invariants of toposes in terms of the theories associated with them or their sites of definition generates a great number of results and notions varying according to the different types of presentation, giving rise to a veritable mathematical morphogenesis.
Book Synopsis Abel’s Theorem in Problems and Solutions by : V.B. Alekseev
Download or read book Abel’s Theorem in Problems and Solutions written by V.B. Alekseev and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.
Book Synopsis Homotopy of Operads and Grothendieck-Teichmuller Groups by : Benoit Fresse
Download or read book Homotopy of Operads and Grothendieck-Teichmuller Groups written by Benoit Fresse and published by American Mathematical Soc.. This book was released on 2017-04-21 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Grothendieck–Teichmüller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this book is to explain that this group has a topological interpretation as a group of homotopy automorphisms associated to the operad of little 2-discs, which is an object used to model commutative homotopy structures in topology. This volume gives a comprehensive survey on the algebraic aspects of this subject. The book explains the definition of an operad in a general context, reviews the definition of the little discs operads, and explains the definition of the Grothendieck–Teichmüller group from the viewpoint of the theory of operads. In the course of this study, the relationship between the little discs operads and the definition of universal operations associated to braided monoidal category structures is explained. Also provided is a comprehensive and self-contained survey of the applications of Hopf algebras to the definition of a rationalization process, the Malcev completion, for groups and groupoids. Most definitions are carefully reviewed in the book; it requires minimal prerequisites to be accessible to a broad readership of graduate students and researchers interested in the applications of operads.
Book Synopsis Topics in Topological Graph Theory by : Lowell W. Beineke
Download or read book Topics in Topological Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2009-07-09 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.
