Fibre Bundles
Title | Fibre Bundles PDF eBook |
Author | D. Husemöller |
Publisher | Springer Science & Business Media |
Pages | 333 |
Release | 2013-06-29 |
Genre | Mathematics |
ISBN | 1475740085 |
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 Fiber Bundle Model
Title | The Fiber Bundle Model PDF eBook |
Author | Alex Hansen |
Publisher | John Wiley & Sons |
Pages | 254 |
Release | 2015-11-02 |
Genre | Science |
ISBN | 352741214X |
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.
Fiber Bundle Techniques in Gauge Theories
Title | Fiber Bundle Techniques in Gauge Theories PDF eBook |
Author | W. Drechsler |
Publisher | Springer |
Pages | 251 |
Release | 2014-03-12 |
Genre | Science |
ISBN | 9783662214657 |
Modern Differential Geometry for Physicists
Title | Modern Differential Geometry for Physicists PDF eBook |
Author | Chris J. Isham |
Publisher | Allied Publishers |
Pages | 308 |
Release | 2002 |
Genre | Geometry, Differential |
ISBN | 9788177643169 |
Fiber Bundles and Homotopy
Title | Fiber Bundles and Homotopy PDF eBook |
Author | Dai Tamaki |
Publisher | |
Pages | 0 |
Release | 2021 |
Genre | Fiber bundles (Mathematics) |
ISBN | 9789811237997 |
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.
Topics in the Homology Theory of Fibre Bundles
Title | Topics in the Homology Theory of Fibre Bundles PDF eBook |
Author | Armand Borel |
Publisher | Springer |
Pages | 100 |
Release | 2006-11-14 |
Genre | Mathematics |
ISBN | 3540349758 |
Lecture Notes on Elementary Topology and Geometry
Title | Lecture Notes on Elementary Topology and Geometry PDF eBook |
Author | I.M. Singer |
Publisher | Springer |
Pages | 240 |
Release | 2015-05-28 |
Genre | Mathematics |
ISBN | 1461573475 |
At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.