On Finite Groups And Homotopy Theory
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On Finite Groups And Homotopy Theory
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Author : Ran Levi
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
On Finite Groups And Homotopy Theory written by Ran Levi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
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.
Homotopy Theory And Its Applications
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Author : Alejandro Adem
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Homotopy Theory And Its Applications written by Alejandro Adem and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This book is the result of a conference held to examine developments in homotopy theory in honor of Samuel Gitler in July 1993 (Cocoyoc, Mexico). It includes several research papers and three expository papers on various topics in homotopy theory. The research papers discuss the following: BL application of homotopy theory to group theory BL fiber bundle theory BL homotopy theory The expository papers consider the following topics: BL the Atiyah-Jones conjecture (by C. Boyer) BL classifying spaces of finite groups (by J. Martino) BL instanton moduli spaces (by J. Milgram) Homotopy Theory and Its Applications offers a distinctive account of how homotopy theoretic methods can be applied to a variety of interesting problems.
Recent Progress In Homotopy Theory
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Author : Donald M. Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Recent Progress In Homotopy Theory written by Donald M. Davis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This volume presents the proceedings from the month-long program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the Japan-U.S. Mathematics Institute (JAMI). The book begins with historical accounts on the work of Professors Peter Landweber and Stewart Priddy. Central among the other topics are the following: 1. classical and nonclassical theory of $H$-spaces, compact groups, and finite groups, 2. classical and chromatic homotopy theory andlocalization, 3. classical and topological Hochschild cohomology, 4. elliptic cohomology and its relation to Moonshine and topological modular forms, and 5. motivic cohomology and Chow rings. This volume surveys the current state of research in these areas and offers an overview of futuredirections.
Algebraic Topology
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Author : Jaume Aguade
language : en
Publisher: Springer
Release Date : 2006-11-15
Algebraic Topology written by Jaume Aguade and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The papers in this collection, all fully refereed, original papers, reflect many aspects of recent significant advances in homotopy theory and group cohomology. From the Contents: A. Adem: On the geometry and cohomology of finite simple groups.- D.J. Benson: Resolutions and Poincar duality for finite groups.- C. Broto and S. Zarati: On sub-A*-algebras of H*V.- M.J. Hopkins, N.J. Kuhn, D.C. Ravenel: Morava K-theories of classifying spaces and generalized characters for finite groups.- K. Ishiguro: Classifying spaces of compact simple lie groups and p-tori.- A.T. Lundell: Concise tables of James numbers and some homotopyof classical Lie groups and associated homogeneous spaces.- J.R. Martino: Anexample of a stable splitting: the classifying space of the 4-dim unipotent group.- J.E. McClure, L. Smith: On the homotopy uniqueness of BU(2) at the prime 2.- G. Mislin: Cohomologically central elements and fusion in groups.
Cohomology Of Finite Groups
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Author : Alejandro Adem
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Cohomology Of Finite Groups written by Alejandro Adem and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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
Homotopy Theoretic Methods In Group Cohomology
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Author : William G. Dwyer
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Homotopy Theoretic Methods In Group Cohomology written by William G. Dwyer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book consists essentially of notes which were written for an Advanced Course on Classifying Spaces and Cohomology of Groups. The course took place at the Centre de Recerca Mathematica (CRM) in Bellaterra from May 27 to June 2, 1998 and was part of an emphasis semester on Algebraic Topology. It consisted of two parallel series of 6 lectures of 90 minutes each and was intended as an introduction to new homotopy theoretic methods in group cohomology. The first part of the book is concerned with methods of decomposing the classifying space of a finite group into pieces made of classifying spaces of appropriate subgroups. Such decompositions have been used with great success in the last 10-15 years in the homotopy theory of classifying spaces of compact Lie groups and p-compact groups in the sense of Dwyer and Wilkerson. For simplicity the emphasis here is on finite groups and on homological properties of various decompositions known as centralizer resp. normalizer resp. subgroup decomposition. A unified treatment of the various decompositions is given and the relations between them are explored. This is preceeded by a detailed discussion of basic notions such as classifying spaces, simplicial complexes and homotopy colimits.
Homotopy Theory Via Algebraic Geometry And Group Representations
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Author : Mark E. Mahowald
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Homotopy Theory Via Algebraic Geometry And Group Representations written by Mark E. Mahowald and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.
Algebraic Topology Of Finite Topological Spaces And Applications
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Author : Jonathan A. Barmak
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-24
Algebraic Topology Of Finite Topological Spaces And Applications written by Jonathan A. Barmak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-24 with Mathematics categories.
This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
Representations Of Finite Groups Local Cohomology And Support
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Author : David J. Benson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-15
Representations Of Finite Groups Local Cohomology And Support written by David J. Benson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-15 with Mathematics categories.
The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas from commutative algebra, cohomology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been Daniel Quillen’s description of the algebraic variety corresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods of algebraic geometry to obtain representation theoretic information. Their work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutative Hopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins’ classification of thick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localizing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approach to address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with ring of operators. The book serves as an introduction to this circle of ideas.
Global Homotopy Theory
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Author : Stefan Schwede
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-06
Global Homotopy Theory written by Stefan Schwede and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-06 with Mathematics categories.
A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.