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Author : Lucian M. Ionescu
Publisher :
ISBN 13 :
Total Pages : 218 pages
Book Rating : 4.:/5 (453 download)
Download or read book Cohomology of Monoidal Categories and Non-abelian Group Cohomology written by Lucian M. Ionescu and published by . This book was released on 2000 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher : Academic Press
ISBN 13 : 0080873464
Total Pages : 289 pages
Book Rating : 4.0/5 (88 download)
Download or read book Cohomology of Groups written by and published by Academic Press. This book was released on 1969 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology of Groups
Author : Karl H. Hofmann
Publisher : Springer Science & Business Media
ISBN 13 : 3642806708
Total Pages : 235 pages
Book Rating : 4.6/5 (428 download)
Download or read book Cohomology Theories for Compact Abelian Groups written by Karl H. Hofmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo metry, the theory of real analytic functions and the theory of differential equations come into the play via Lie group theory; point set topology is used in describing the local geometric structure of compact groups via limit spaces; global topology and the theory of manifolds again playa role through Lie group theory; and, of course, algebra enters through the cohomology and homology theory. A particularly well understood subclass of compact groups is the class of com pact abelian groups. An added element of elegance is the duality theory, which states that the category of compact abelian groups is completely equivalent to the category of (discrete) abelian groups with all arrows reversed. This allows for a virtually complete algebraisation of any question concerning compact abelian groups. The subclass of compact abelian groups is not so special within the category of compact. groups as it may seem at first glance. As is very well known, the local geometric structure of a compact group may be extremely complicated, but all local complication happens to be "abelian". Indeed, via the duality theory, the complication in compact connected groups is faithfully reflected in the theory of torsion free discrete abelian groups whose notorious complexity has resisted all efforts of complete classification in ranks greater than two.
Author : Domenico Fiorenza
Publisher : World Scientific
ISBN 13 : 9811276714
Total Pages : 248 pages
Book Rating : 4.8/5 (112 download)
Download or read book Character Map In Non-abelian Cohomology, The: Twisted, Differential, And Generalized written by Domenico Fiorenza and published by World Scientific. This book was released on 2023-08-11 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel development of fundamental and fascinating aspects of algebraic topology and mathematical physics: 'extra-ordinary' and further generalized cohomology theories enhanced to 'twisted' and differential-geometric form, with focus on, firstly, their rational approximation by generalized Chern character maps, and then, the resulting charge quantization laws in higher n-form gauge field theories appearing in string theory and the classification of topological quantum materials.Although crucial for understanding famously elusive effects in strongly interacting physics, the relevant higher non-abelian cohomology theory ('higher gerbes') has had an esoteric reputation and remains underdeveloped.Devoted to this end, this book's theme is that various generalized cohomology theories are best viewed through their classifying spaces (or moduli stacks) — not necessarily infinite-loop spaces — from which perspective the character map is really an incarnation of the fundamental theorem of rational homotopy theory, thereby not only uniformly subsuming the classical Chern character and a multitude of scattered variants that have been proposed, but now seamlessly applicable in the hitherto elusive generality of (twisted, differential, and) non-abelian cohomology.In laying out this result with plenty of examples, this book provides a modernized introduction and review of fundamental classical topics: 1. abstract homotopy theory via model categories; 2. generalized cohomology in its homotopical incarnation; 3. rational homotopy theory seen via homotopy Lie theory, whose fundamental theorem we recast as a (twisted) non-abelian de Rham theorem, which naturally induces the (twisted) non-abelian character map.
Author : Alejandro Adem
Publisher : Springer Science & Business Media
ISBN 13 : 3662062828
Total Pages : 333 pages
Book Rating : 4.6/5 (62 download)
Download or read book Cohomology of Finite Groups written by Alejandro Adem and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important new fields in mathematics, like homological algebra and algebraic K-theory. This is the first book to deal comprehensively with the cohomology of finite groups: it introduces the most important and useful algebraic and topological techniques, and describes the interplay of the subject with those of homotopy theory, representation theory and group actions. The combination of theory and examples, together with the techniques for computing the cohomology of important classes of groups including symmetric groups, alternating groups, finite groups of Lie type, and some of the sporadic simple groups, enable readers to acquire an in-depth understanding of group cohomology and its extensive applications.
Author : Jon F. Carlson
Publisher : Springer Science & Business Media
ISBN 13 : 9401702152
Total Pages : 782 pages
Book Rating : 4.4/5 (17 download)
Download or read book Cohomology Rings of Finite Groups written by Jon F. Carlson and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num ber theory, and it grew into an integral component of algebraic topology. In the last thirty years, group cohomology has developed a powerful con nection with finite group representations. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in teractions with representation theory involve cohomology rings and the geometry of spectra over these rings. It is this connection to represen tation theory that we take as our primary motivation for this book. The book consists of two separate pieces. Chronologically, the first part was the computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64. The ideas and the programs for the calculations were developed over the last 10 years. Several new features were added over the course of that time. We had originally planned to include only a brief introduction to the calculations. However, we were persuaded to produce a more substantial text that would include in greater detail the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the com putations. We have gathered together many of the results and ideas that are the focus of the calculations from throughout the mathematical literature.
Author : David J. Green
Publisher : Springer Science & Business Media
ISBN 13 : 9783540203391
Total Pages : 156 pages
Book Rating : 4.2/5 (33 download)
Download or read book Gröbner Bases and the Computation of Group Cohomology written by David J. Green and published by Springer Science & Business Media. This book was released on 2003-11-18 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops the Gröbner basis methods needed to perform efficient state of the art calculations in the cohomology of finite groups. Results obtained include the first counterexample to the conjecture that the ideal of essential classes squares to zero. The context is J. F. Carlson’s minimal resolutions approach to cohomology computations.
Author : Serge Lang
Publisher : Springer
ISBN 13 : 3540683372
Total Pages : 231 pages
Book Rating : 4.5/5 (46 download)
Download or read book Topics in Cohomology of Groups written by Serge Lang and published by Springer. This book was released on 2006-11-14 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a mostly translated reprint of a report on cohomology of groups from the 1950s and 1960s, originally written as background for the Artin-Tate notes on class field theory, following the cohomological approach. This report was first published (in French) by Benjamin. For this new English edition, the author added Tate's local duality, written up from letters which John Tate sent to Lang in 1958 - 1959. Except for this last item, which requires more substantial background in algebraic geometry and especially abelian varieties, the rest of the book is basically elementary, depending only on standard homological algebra at the level of first year graduate students.
Author : Antonio M. Cegarra
Publisher : Springer Nature
ISBN 13 : 3031502582
Total Pages : 227 pages
Book Rating : 4.0/5 (315 download)
Download or read book The Cohomology of Monoids written by Antonio M. Cegarra and published by Springer Nature. This book was released on 2024 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: This monograph covers topics in the cohomology of monoids up through recent developments. Jonathan Leech's original monograph in the Memoirs of the American Mathematical Society dates back to 1975. This book is an organized, accessible, and self-contained account of this cohomology that includes more recent significant developments that were previously scattered among various publications, along with completely new material. It summarizes the original Leech theory and provides a modern and thorough treatment of the cohomological classification of coextensions of both monoids and monoidal groupoids, including the case of monoids with operators. This cohomology is also compared to the classical Eilenberg-Mac Lane and Hochschild-Mitchell cohomologies. Connections are also established with the Lausch-Loganathan cohomology theory for inverse semigroups, the Gabriel-Zisman cohomology of simplicial sets, the Wells cohomology of small categories (also known as Baues-Wirsching cohomology), Grothendieck sheaf cohomology, and finally Beck's triple cohomology. It also establishes connections with Grillet's cohomology theory for commutative semigroups. The monograph is aimed at researchers in the theory of monoids, or even semigroups, and its interface with category theory, homological algebra, and related fields. However, it is also written to be accessible to graduate students in mathematics and mathematicians in general
Author : Kenneth S. Brown
Publisher : Springer Science & Business Media
ISBN 13 : 1468493272
Total Pages : 318 pages
Book Rating : 4.4/5 (684 download)
Download or read book Cohomology of Groups written by Kenneth S. Brown and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.
Author : Karl Heinrich Hofmann
Publisher :
ISBN 13 : 9780387057309
Total Pages : 236 pages
Book Rating : 4.0/5 (573 download)
Download or read book Cohomology Theories for Compact Abelian Groups written by Karl Heinrich Hofmann and published by . This book was released on 1973 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jean H Gallier
Publisher : World Scientific
ISBN 13 : 9811245045
Total Pages : 799 pages
Book Rating : 4.8/5 (112 download)
Download or read book Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry written by Jean H Gallier and published by World Scientific. This book was released on 2022-01-19 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.
Author : Akira Kōno
Publisher : American Mathematical Soc.
ISBN 13 : 9780821835142
Total Pages : 276 pages
Book Rating : 4.8/5 (351 download)
Download or read book Generalized Cohomology written by Akira Kōno and published by American Mathematical Soc.. This book was released on 2006 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to give an exposition of generalized (co)homology theories that can be read by a group of mathematicians who are not experts in algebraic topology. This title starts with basic notions of homotopy theory, and introduces the axioms of generalized (co)homology theory. It also discusses various types of generalized cohomology theories.
Author : Lekh R. Vermani
Publisher :
ISBN 13 :
Total Pages : 162 pages
Book Rating : 4.3/5 (91 download)
Download or read book Lectures on Cohomology of Groups written by Lekh R. Vermani and published by . This book was released on 1994 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : S. I. Andersson
Publisher :
ISBN 13 : 9789971500139
Total Pages : 280 pages
Book Rating : 4.5/5 (1 download)
Download or read book Non-Abelian Cohomology Theory and Applications to the Yang-Mills and Backlund Problems written by S. I. Andersson and published by . This book was released on 1994 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pierre Antoine Grillet
Publisher : Springer Nature
ISBN 13 : 3031082125
Total Pages : 191 pages
Book Rating : 4.0/5 (31 download)
Download or read book The Cohomology of Commutative Semigroups written by Pierre Antoine Grillet and published by Springer Nature. This book was released on 2022-09-28 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an organized exposition of the current state of the theory of commutative semigroup cohomology, a theory which was originated by the author and has matured in the past few years. The work contains a fundamental scientific study of questions in the theory. The various approaches to commutative semigroup cohomology are compared. The problems arising from definitions in higher dimensions are addressed. Computational methods are reviewed. The main application is the computation of extensions of commutative semigroups and their classification. Previously the components of the theory were scattered among a number of research articles. This work combines all parts conveniently in one volume. It will be a valuable resource for future students of and researchers in commutative semigroup cohomology and related areas.
Author : Burt Totaro
Publisher : Cambridge University Press
ISBN 13 : 1107015774
Total Pages : 245 pages
Book Rating : 4.1/5 (7 download)
Download or read book Group Cohomology and Algebraic Cycles written by Burt Totaro and published by Cambridge University Press. This book was released on 2014-06-26 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.
