Fibre Bundles
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Fibre Bundles
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Author : Dale Husemöller
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Fibre Bundles written by Dale Husemöller 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.
Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. The new edition of this text includes two additional chapters, one on the gauge group of a bundle and the other on the differential forms representing characteristic classes of complex vector bundles on manifolds.
Fibre Bundles
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Author : D. Husemöller
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Fibre Bundles written by D. Husemöller 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 2013-06-29 with Mathematics categories.
The notion of a fibre bundle first arose out of questions posed in the 1930s on the topology and geometry of manifolds. By the year 1950 the defini tion of fibre bundle had been clearly formulated, the homotopy classifica tion of fibre bundles achieved, and the theory of characteristic classes of fibre bundles developed by several mathematicians, Chern, Pontrjagin, Stiefel, and Whitney. Steenrod's book, which appeared in 1950, gave a coherent treatment of the subject up to that time. About 1955 Milnor gave a construction of a universal fibre bundle for any topological group. This construction is also included in Part I along with an elementary proof that the bundle is universal. During the five years from 1950 to 1955, Hirzebruch clarified the notion of characteristic class and used it to prove a general Riemann-Roch theorem for algebraic varieties. This was published in his Ergebnisse Monograph. A systematic development of characteristic classes and their applications to manifolds is given in Part III and is based on the approach of Hirze bruch as modified by Grothendieck.
The Topology Of Fibre Bundles
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Author : Norman Steenrod
language : en
Publisher: Princeton University Press
Release Date : 1999-04-25
The Topology Of Fibre Bundles written by Norman Steenrod and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-25 with Mathematics categories.
Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically. It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.
Topics In The Homology Theory Of Fibre Bundles
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Author : Armand Borel
language : en
Publisher: Springer
Release Date : 2006-11-14
Topics In The Homology Theory Of Fibre Bundles written by Armand Borel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Introduction To Fibre Bundles
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Author : Richard Dawson Porter
language : en
Publisher:
Release Date : 1977
Introduction To Fibre Bundles written by Richard Dawson Porter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Fiber bundles (Mathematics). categories.
The Topology Of Fibre Bundles
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Author : Norman E. Steenrod
language : en
Publisher:
Release Date : 1970
The Topology Of Fibre Bundles written by Norman E. Steenrod and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
Introduction To Fibre Bundles
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Author : Richard D. Porter
language : en
Publisher:
Release Date :
Introduction To Fibre Bundles written by Richard D. Porter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Riemannian Geometry Fiber Bundles Kaluza Klein Theories And All That
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Author : Robert Coquereaux
language : en
Publisher: World Scientific
Release Date : 1988
Riemannian Geometry Fiber Bundles Kaluza Klein Theories And All That written by Robert Coquereaux and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
This book discusses the geometrical aspects of Kaluza-Klein theories. The ten chapters cover topics from the differential and Riemannian manifolds to the reduction of Einstein-Yang-Mills action. It would definitely prove interesting reading to physicists and mathematicians, theoretical and experimental.
Lectures On Fibre Bundles And Differential Geometry
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Author : J.L. Koszul
language : en
Publisher: Springer
Release Date : 1987
Lectures On Fibre Bundles And Differential Geometry written by J.L. Koszul and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
The main topic of these notes is the theory of connections. There are two basic notions in the theory: the notion of covariant derivation which concerns differentiable sections of vector bundles, and th~ notion of connection forms on principal bundles. These two notions Hre by no means independent of each other. While any law of covariant derivation in a vector bundle can be defined by a connection forn in the princip21 bundle of framee, an independent treatment of covariant doriv~tions is desirable in view of many applications wh~re the principal bundle remains in the background. In the first chapter, we start with an algebraic formulation of covariant derivations. The rela"i:,ed notions of curvature, differen tials and torsion are discussed without reference to manifolds. Chapters II, III and IV are devoted to a study of connection forms on principal bundles. Chapter V deals essentially with the relations bet ween covariant derivations and co:mcction forms. Some special features of the theory of connections in almost complex and holomorphic bundles, which include the recent results of Atiyah ~2-1 form the subject matter of the final chapter. We have not dealt with any topic related to the theory of characteristic forms or that of "Cartan connections" in the sense of 11 Ehresmann, but a few referencos in these directions are given in the bibliography.
Fiber Bundles And Homotopy
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Author : Dai Tamaki
language : en
Publisher:
Release Date : 2021
Fiber Bundles And Homotopy written by Dai Tamaki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Fiber bundles (Mathematics) categories.
This book is an introduction to fiber bundles and fibrations. But the ultimate goal is to make the reader feel comfortable with basic ideas in homotopy theory. The author found that the classification of principal fiber bundles is an ideal motivation for this purpose. The notion of homotopy appears naturally in the classification. Basic tools in homotopy theory such as homotopy groups and their long exact sequence need to be introduced. Furthermore, the notion of fibrations, which is one of three important classes of maps in homotopy theory, can be obtained by extracting the most essential properties of fiber bundles. The book begins with elementary examples and then gradually introduces abstract definitions when necessary. The reader is assumed to be familiar with point-set topology, but it is the only requirement for this book.