Characteristic Classes
DOWNLOAD
FREE 30 Days
Download Characteristic Classes PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Characteristic Classes book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Characteristic Classes
DOWNLOAD
FREE 30 Days
Author : John Willard Milnor
language : en
Publisher: Princeton University Press
Release Date : 1974
Characteristic Classes written by John Willard Milnor 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 1974 with Mathematics categories.
The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
Curvature And Characteristic Classes
DOWNLOAD
FREE 30 Days
Author : J.L. Dupont
language : en
Publisher: Springer
Release Date : 2006-11-15
Curvature And Characteristic Classes written by J.L. Dupont 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.
Characteristic Classes Am 76 Volume 76
DOWNLOAD
FREE 30 Days
Author : John Milnor
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Characteristic Classes Am 76 Volume 76 written by John Milnor 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 2016-03-02 with Mathematics categories.
The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
Geometry Of Characteristic Classes
DOWNLOAD
FREE 30 Days
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.
The Theory Of Characteristic Classes
DOWNLOAD
FREE 30 Days
Author : John Willard Milnor
language : en
Publisher:
Release Date : 1959
The Theory Of Characteristic Classes written by John Willard Milnor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Topology categories.
Differential Geometry
DOWNLOAD
FREE 30 Days
Author : Loring W. Tu
language : en
Publisher: Springer
Release Date : 2017-06-01
Differential Geometry written by Loring W. Tu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-01 with Mathematics categories.
This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text. Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included. Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.
Characteristic Classes And The Cohomology Of Finite Groups
DOWNLOAD
FREE 30 Days
Author : C. B. Thomas
language : en
Publisher: Cambridge University Press
Release Date : 2008-11-27
Characteristic Classes And The Cohomology Of Finite Groups written by C. B. Thomas 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 2008-11-27 with Mathematics categories.
The purpose of this book is to study the relation between the representation ring of a finite group and its integral cohomology by means of characteristic classes. In this way it is possible to extend the known calculations and prove some general results for the integral cohomology ring of a group G of prime power order. Among the groups considered are those of p-rank less than 3, extra-special p-groups, symmetric groups and linear groups over finite fields. An important tool is the Riemann - Roch formula which provides a relation between the characteristic classes of an induced representation, the classes of the underlying representation and those of the permutation representation of the infinite symmetric group. Dr Thomas also discusses the implications of his work for some arithmetic groups which will interest algebraic number theorists. Dr Thomas assumes the reader has taken basic courses in algebraic topology, group theory and homological algebra, but has included an appendix in which he gives a purely topological proof of the Riemann - Roch formula.
Fibre Bundles
DOWNLOAD
FREE 30 Days
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.
Symplectic Geometry And Secondary Characteristic Classes
DOWNLOAD
FREE 30 Days
Author : Izu Vaisman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Symplectic Geometry And Secondary Characteristic Classes written by Izu Vaisman 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 2013-12-01 with Mathematics categories.
The present work grew out of a study of the Maslov class (e. g. (37]), which is a fundamental invariant in asymptotic analysis of partial differential equations of quantum physics. One of the many in terpretations of this class was given by F. Kamber and Ph. Tondeur (43], and it indicates that the Maslov class is a secondary characteristic class of a complex trivial vector bundle endowed with a real reduction of its structure group. (In the basic paper of V. I. Arnold about the Maslov class (2], it is also pointed out without details that the Maslov class is characteristic in the category of vector bundles mentioned pre viously. ) Accordingly, we wanted to study the whole range of secondary characteristic classes involved in this interpretation, and we gave a short description of the results in (83]. It turned out that a complete exposition of this theory was rather lengthy, and, moreover, I felt that many potential readers would have to use a lot of scattered references in order to find the necessary information from either symplectic geometry or the theory of the secondary characteristic classes. On the otherhand, both these subjects are of a much larger interest in differential geome try and topology, and in the applications to physical theories.
Loop Spaces Characteristic Classes And Geometric Quantization
DOWNLOAD
FREE 30 Days
Author : Jean-Luc Brylinski
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-30
Loop Spaces Characteristic Classes And Geometric Quantization written by Jean-Luc Brylinski 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 2009-12-30 with Mathematics categories.
This book examines the differential geometry of manifolds, loop spaces, line bundles and groupoids, and the relations of this geometry to mathematical physics. Applications presented in the book involve anomaly line bundles on loop spaces and anomaly functionals, central extensions of loop groups, Kähler geometry of the space of knots, and Cheeger--Chern--Simons secondary characteristics classes. It also covers the Dirac monopole and Dirac’s quantization of the electrical charge.