Cohomology Operations and Modular Invariant Theory PDF Download

Author: L. Lomonaco
Publisher:
ISBN:
Category :
Languages : en
Pages : 13

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Author: Robert E. Mosher
Publisher: Courier Corporation
ISBN: 0486466647
Category : Mathematics
Languages : en
Pages : 226

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Book Description
Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.

Author: H.E.A. Eddy Campbell
Publisher: Springer
ISBN: 9783642174056
Category : Mathematics
Languages : en
Pages : 234

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Book Description
This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers—an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.

Author: H.E.A. Eddy Campbell
Publisher: Springer Science & Business Media
ISBN: 3642174043
Category : Mathematics
Languages : en
Pages : 233

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Book Description
This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers—an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.

Author: John R. Harper
Publisher: American Mathematical Soc.
ISBN: 0821831984
Category : Mathematics
Languages : en
Pages : 282

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Book Description
Although the theory and applications of secondary cohomology operations are an important part of an advanced graduate-level algebraic topology course, there are few books on the subject. The AMS now fills that gap with the publication of the present volume. The author's main purpose in this book is to develop the theory of secondary cohomology operations for singular cohomology theory, which is treated in terms of elementary constructions from general homotopy theory. Among manyapplications considered are the Hopf invariant one theorem (for all primes $p$, including $p = 2$), Browder's theorem on higher Bockstein operations, and cohomology theory of Massey-Peterson fibrations. Numerous examples and exercises help readers to gain a working knowledge of the theory. A summary ofmore advanced parts of the core material is included in the first chapter. Prerequisite is basic algebraic topology, including the Steenrod operations. The book is geared toward graduate students and research mathematicians interested in algebraic topology and can be used for self-study or as a textbook for an advanced course on the topic. It is available in both hardcover and softcover editions.

Author: Mara D. Neusel
Publisher: American Mathematical Soc.
ISBN: 0821849816
Category : Mathematics
Languages : en
Pages : 384

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Book Description
The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.

Author: Alejandro Adem
Publisher: Springer Science & Business Media
ISBN: 3662062801
Category : Mathematics
Languages : en
Pages : 329

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Book Description
Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homo logical algebra and algebraic K-theory. It arose primarily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the meanings of the low dimensional homology groups of a space X. For example, if the universal cover of X was three connected, it was known that H2(X; A. ) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N

Author: David B.A. Epstein
Publisher: Princeton University Press
ISBN: 1400881676
Category : Mathematics
Languages : en
Pages : 152

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Book Description
Written and revised by D. B. A. Epstein.

Author: Norman Earl Steenrod
Publisher: Princeton University Press
ISBN: 9780691079240
Category : Homology theory
Languages : en
Pages : 164

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Author: D. J. Benson
Publisher: Cambridge University Press
ISBN: 9780521636520
Category : Mathematics
Languages : en
Pages : 296

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Book Description
A further introduction to modern developments in the representation theory of finite groups and associative algebras.