Principal Fibrations
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Principal Fibrations
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Author : JEAN-PIERRE. MAYER
language : en
Publisher:
Release Date : 1960
Principal Fibrations written by JEAN-PIERRE. MAYER and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with categories.
AD-2 0 5679 AD-260 568Div. 15U (3 Aug 61) OTS price $1.60 Johns Hopkins U., Baltimore, Md. P INCIPAL FIBRATIONS, b Jean-Pierre Mayer. 1960, 12p. (Contract DA 36-034-ORD-3299) (AROD-2799:1)Unclassified report DESCRIPTORS: *Algebraic topology, Groups (Mathematics). A fibration ith an Eilenberg-MacLane space of type (pi, n), n greater than 1, as fiber and simply-connected base is equivalent to one induced from a path-space fibration by a map of the base into an Eilenberg-MacLane space of type (pi, n + 1). For the purposes of this paper, and by analogy with the classification theory of fiber-bundles, this is called a fabrication principal. T e problem considered the conditions under which a fibration with a loop-space as fiber is equivalent to a principal one. (Author).
Classifying Spaces And Fibrations
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Author : J. Peter May
language : en
Publisher: American Mathematical Soc.
Release Date : 1975
Classifying Spaces And Fibrations written by J. Peter May 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 1975 with Classifying spaces categories.
The basic theory of fibrations is generalized to a context in which fibres, and maps on fibres, are constrained to lie in any preassigned category of spaces [script capital] F. Then axioms are placed on [script capital] F to allow the development of a theory of associated principal fibrations and, under several choices of additional hypotheses on [script capital] F, a classification theorem is proven for such fibrations.
Topology For Physicists
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Author : Albert S. Schwarz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Topology For Physicists written by Albert S. Schwarz 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 2013-03-09 with Mathematics categories.
In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equa tions of motion (solitons and instantons) allow the physicist to leave the frame work of perturbation theory. The significance of topology has increased even further with the development of string theory, which uses very sharp topologi cal methods-both in the study of strings, and in the pursuit of the transition to four-dimensional field theories by means of spontaneous compactification. Im portant applications of topology also occur in other areas of physics: the study of defects in condensed media, of singularities in the excitation spectrum of crystals, of the quantum Hall effect, and so on. Nowadays, a working knowledge of the basic concepts of topology is essential to quantum field theorists; there is no doubt that tomorrow this will also be true for specialists in many other areas of theoretical physics. The amount of topological information used in the physics literature is very large. Most common is homotopy theory. But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds.
The Moore Spectral Sequence For Principal Fibrations
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Author : Dogan Donmez
language : en
Publisher:
Release Date : 1979
The Moore Spectral Sequence For Principal Fibrations written by Dogan Donmez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Fiber bundles (Mathematics) categories.
Obstruction Theory
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Author : H. J. Baues
language : en
Publisher: Springer
Release Date : 2006-11-15
Obstruction Theory written by H. J. Baues 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.
Simplicial Homotopy Theory
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Author : Paul G. Goerss
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Simplicial Homotopy Theory written by Paul G. Goerss 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.
Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.
Algebraic K Theory
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Author : Grzegorz Banaszak
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Algebraic K Theory written by Grzegorz Banaszak 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 1996 with Mathematics categories.
This book contains proceedings of the research conference on algebraic K-theory which took place in Poznan, Poland in September 1995. The conference concluded the activity of the algebraic K-theory seminar held at the Adam Mickiewicz University in the academic year 1994-1995. Talks at the conference covered a wide range of current research activities in algebraic K-theory. In particular, the following topics were covered * K-theory of fields and rings of integers * K-theory of elliptic and modular curves * Theory of motives, motivic cohomology, Beilinson conjectures * algebraic K-theory of topological spaces, topological Hochschild homology and cyclic homology. With contributions by leading experts in the field, this book provides a look at the state of current research in algebraic K-theory.
Geometry Of Characteristic Classes
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Author : Shigeyuki Morita
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Geometry Of Characteristic Classes written by Shigeyuki Morita 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 2001 with Mathematics categories.
Characteristic classes are central to the modern study of the topology and geometry of manifolds. They were first introduced in topology, where, for instance, they could be used to define obstructions to the existence of certain fiber bundles. Characteristic classes were later defined (via the Chern-Weil theory) using connections on vector bundles, thus revealing their geometric side. In the late 1960s new theories arose that described still finer structures. Examples of the so-called secondary characteristic classes came from Chern-Simons invariants, Gelfand-Fuks cohomology, and the characteristic classes of flat bundles. The new techniques are particularly useful for the study of fiber bundles whose structure groups are not finite dimensional. The theory of characteristic classes of surface bundles is perhaps the most developed. Here the special geometry of surfaces allows one to connect this theory to the theory of moduli space of Riemann surfaces, i.e., Teichmüller theory. In this book Morita presents an introduction to the modern theories of characteristic classes.
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
Algebraic Homotopy
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Author : Hans J. Baues
language : en
Publisher: Cambridge University Press
Release Date : 1989-02-16
Algebraic Homotopy written by Hans J. Baues 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 1989-02-16 with Mathematics categories.
This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra.