Homology of Classical Groups Over Finite Fields and Their Associated Infinite Loop Spaces PDF Download
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Author: Z. Fiedorowicz
Publisher: Springer
ISBN: 3540357351
Category : Mathematics
Languages : en
Pages : 441
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Book Description
Author: Z. Fiedorowicz
Publisher: Springer
ISBN: 3540357351
Category : Mathematics
Languages : en
Pages : 441
Get Book Here
Book Description
Author: Z. Fiedorowicz
Publisher:
ISBN: 9783662192436
Category :
Languages : en
Pages : 444
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Book Description
Author: Zbigniew Fiedorowicz
Publisher:
ISBN:
Category :
Languages : de
Pages :
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Book Description
Author: Zbigniew Fiedorowicz
Publisher:
ISBN:
Category : Finite groups
Languages : en
Pages : 174
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Book Description
Author: Alejandro Adem
Publisher: American Mathematical Soc.
ISBN: 0821806580
Category : Mathematics
Languages : en
Pages : 549
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Book Description
This volume combines contributions in topology and representation theory that reflect the increasingly vigorous interactions between these areas. Topics such as group theory, homotopy theory, cohomology of groups, and modular representations are covered. All papers have been carefully refereed and offer lasting value.
Author: Carles Broto
Publisher: Birkhäuser
ISBN: 3034890184
Category : Mathematics
Languages : en
Pages : 405
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Book Description
Central to this collection of papers are new developments in the general theory of localization of spaces. This field has undergone tremendous change of late and is yielding new insight into the mysteries of classical homotopy theory. The present volume comprises the refereed articles submitted at the Conference on Algebraic Topology held in Sant Feliu de Guíxols, Spain, in June 1994. Several comprehensive articles on general localization clarify the basic tools and give a report on the state of the art in the subject matter. The text is therefore accessible not only to the professional mathematician but also to the advanced student.
Author: Samuel N. Kleinerman
Publisher: American Mathematical Soc.
ISBN: 0821822683
Category : Mathematics
Languages : en
Pages : 93
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Book Description
Author: Alejandro Adem
Publisher: Springer Science & Business Media
ISBN: 9783540202837
Category : Mathematics
Languages : en
Pages : 338
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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: Ran Levi
Publisher: American Mathematical Soc.
ISBN: 0821804014
Category : Mathematics
Languages : en
Pages : 121
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Book Description
In part 1 we study the homology, homotopy, and stable homotopy of [capital Greek]Omega[italic capital]B[lowercase Greek]Pi[up arrowhead][over][subscript italic]p, where [italic capital]G is a finite [italic]p-perfect group. In part 2 we define the concept of resolutions by fibrations over an arbitrary family of spaces.
Author: Vincent Franjou
Publisher: Birkhäuser
ISBN: 3319213059
Category : Mathematics
Languages : en
Pages : 154
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Book Description
This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems. In the lectures by Aurélien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament’s theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko’s unpublished results. The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert’s fourteenth problem and its solution to the context of cohomology. The focus here is on the cohomology of algebraic groups, or rational cohomology, and the coefficients are Friedlander and Suslin’s strict polynomial functors, a conceptual form of modules over the Schur algebra. Roman Mikhailov’s lectures highlight topological invariants: homoto py and homology of topological spaces, through derived functors of polynomial functors. In this regard the functor framework makes better use of naturality, allowing it to reach calculations that remain beyond the grasp of classical algebraic topology. Lastly, Antoine Touzé’s introductory course on homological algebra makes the book accessible to graduate students new to the field. The links between functor homology and the three fields mentioned above offer compelling arguments for pushing the development of the functor viewpoint. The lectures in this book will provide readers with a feel for functors, and a valuable new perspective to apply to their favourite problems.
