Fibre Bundles

Author : D. Husemöller
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 43,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475740080

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Fibre Bundles by D. Husemöller Pdf

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.

Author : Armand Borel
Publisher : Springer
Page : 100 pages
File Size : 45,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540349754

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Topics in the Homology Theory of Fibre Bundles by Armand Borel Pdf

Author : Dale Husemöller
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 42,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475722611

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Fibre Bundles by Dale Husemöller Pdf

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.

Author : Norman E. Steenrod
Publisher : Unknown
Page : 227 pages
File Size : 54,7 Mb
Release : 1970
Category : Electronic
ISBN : OCLC:934395389

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The Topology of Fibre Bundles by Norman E. Steenrod Pdf

Author : Steinar Johannesen
Publisher : CRC Press
Page : 400 pages
File Size : 55,5 Mb
Release : 2016-12-08
Category : Mathematics
ISBN : 9781315342627

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Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics by Steinar Johannesen Pdf

This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics provides complete and rigorous proofs of all the results presented within. Among the themes illustrated in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. It can be used as a textbook for a pure mathematics course in differential geometry, assuming the reader has a good understanding of basic analysis, linear algebra and point set topology. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories.

Author : Dai Tamaki
Publisher : Unknown
Page : 0 pages
File Size : 46,6 Mb
Release : 2021
Category : Fiber bundles (Mathematics)
ISBN : 9811237999

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Fiber Bundles and Homotopy by Dai Tamaki Pdf

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.

Author : Norman Steenrod
Publisher : Princeton University Press
Page : 241 pages
File Size : 40,7 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9781400883875

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The Topology of Fibre Bundles. (PMS-14), Volume 14 by Norman Steenrod Pdf

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.

Author : Steinar Johannesen
Publisher : CRC Press
Page : 652 pages
File Size : 47,8 Mb
Release : 2016-12-08
Category : Mathematics
ISBN : 9781498796729

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Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics by Steinar Johannesen Pdf

This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Written to be self-contained, this book provides complete and rigorous proofs of all the results presented within. Among the themes illustrated in the book are differentiable manifolds, differential forms, fiber bundles and differential geometry with non-trivial applications especially within the general theory of relativity. The emphasis is upon a systematic and logical construction of the mathematical foundations. It can be used as a textbook for a pure mathematics course in differential geometry, assuming the reader has a good understanding of basic analysis, linear algebra and point set topology. The book will also appeal to students of theoretical physics interested in the mathematical foundation of the theories.

Author : Chris J. Isham
Publisher : Allied Publishers
Page : 308 pages
File Size : 52,5 Mb
Release : 2002
Category : Geometry, Differential
ISBN : 8177643169

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Modern Differential Geometry for Physicists by Chris J. Isham Pdf

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 2024-06-15
Category : Electronic
ISBN : 9789814507691

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Riemannian Geometry, Fiber Bundles, Kaluza-Klein Theories and All That? by Anonim Pdf

Author : A. P. Balachandran,G. Marmo,B. S. Skagerstam
Publisher : Unknown
Page : 152 pages
File Size : 46,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662164094

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Gauge Symmetries and Fibre Bundles by A. P. Balachandran,G. Marmo,B. S. Skagerstam Pdf

Author : Alex Hansen,Per Christian Hemmer,Srutarshi Pradhan
Publisher : John Wiley & Sons
Page : 254 pages
File Size : 45,7 Mb
Release : 2015-11-02
Category : Science
ISBN : 9783527412143

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The Fiber Bundle Model by Alex Hansen,Per Christian Hemmer,Srutarshi Pradhan Pdf

Gathering research from physics, mechanical engineering, and statistics in a single resource for the first time, this text presents the background to the model, its theoretical basis, and applications ranging from materials science to earth science. The authors start by explaining why disorder is important for fracture and then go on to introduce the fiber bundle model, backed by various different applications. Appendices present the necessary mathematical, computational and statistical background required. The structure of the book allows the reader to skip some material that is too specialized, making this topic accessible to the engineering, mechanics and materials science communities, in addition to providing further reading for graduate students in statistical physics.

Author : Reinhold A. Bertlmann
Publisher : Oxford University Press
Page : 590 pages
File Size : 46,5 Mb
Release : 2000-11-02
Category : Science
ISBN : 0198507623

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Anomalies in Quantum Field Theory by Reinhold A. Bertlmann Pdf

This text presents the different aspects of the study of anomalies. Much emphasis is now being placed on the formulation of the theory using the mathematical ideas of differential geometry and topology. It includes derivations and calculations

Author : Pratip Bhattacharyya,Bikas K. Chakrabarti
Publisher : Springer
Page : 527 pages
File Size : 40,6 Mb
Release : 2006-09-10
Category : Science
ISBN : 9783540353751

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Modelling Critical and Catastrophic Phenomena in Geoscience by Pratip Bhattacharyya,Bikas K. Chakrabarti Pdf

This book presents a broad survey of models for critical and catastrophic phenomena in the geosciences, with strong emphasis on earthquakes. It assumes the perspective of statistical physics, which provides the theoretical frame for dealing with complex systems in general. This volume addresses graduate students wishing to specialize in the field and researchers working or interested in the field having a background in the physics, geosciences or applied mathematics.

Author : Norman Steenrod
Publisher : Princeton University Press
Page : 242 pages
File Size : 45,8 Mb
Release : 1999-04-25
Category : Mathematics
ISBN : 0691005486

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The Topology of Fibre Bundles by Norman Steenrod Pdf

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.