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Characteristic Classes

Characteristic Classes PDF
Author: John Willard Milnor
Publisher: Princeton University Press
ISBN: 9780691081229
Size: 44.75 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 330
View: 3810

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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

Geometry of Characteristic Classes PDF
Author: Shigeyuki Morita
Publisher: American Mathematical Soc.
ISBN: 0821821393
Size: 27.97 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 185
View: 7446

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This is an inexpensive paper volume that will appeal to upper level students. Professor Morita is a world-class authority on this topic.

Symplectic Geometry And Secondary Characteristic Classes

Symplectic Geometry and Secondary Characteristic Classes PDF
Author: Izu Vaisman
Publisher: Springer Science & Business Media
ISBN: 1475719604
Size: 72.82 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 216
View: 2849

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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

Loop Spaces  Characteristic Classes and Geometric Quantization PDF
Author: Jean-Luc Brylinski
Publisher: Springer Science & Business Media
ISBN: 0817647317
Size: 23.11 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 302
View: 4738

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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.

Nilpotent Orbits Primitive Ideals And Characteristic Classes

Nilpotent Orbits  Primitive Ideals  and Characteristic Classes PDF
Author: Walter Borho
Publisher: Springer Science & Business Media
ISBN: 1461245583
Size: 55.21 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 134
View: 7773

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1. The Subject Matter. Consider a complex semisimple Lie group G with Lie algebra g and Weyl group W. In this book, we present a geometric perspective on the following circle of ideas: polynomials The "vertices" of this graph are some of the most important objects in representation theory. Each has a theory in its own right, and each has had its own independent historical development. - A nilpotent orbit is an orbit of the adjoint action of G on g which contains the zero element of g in its closure. (For the special linear group 2 G = SL(n,C), whose Lie algebra 9 is all n x n matrices with trace zero, an adjoint orbit consists of all matrices with a given Jordan canonical form; such an orbit is nilpotent if the Jordan form has only zeros on the diagonal. In this case, the nilpotent orbits are classified by partitions of n, given by the sizes of the Jordan blocks.) The closures of the nilpotent orbits are singular in general, and understanding their singularities is an important problem. - The classification of irreducible Weyl group representations is quite old.

Characteristic Classes Am 76 Volume 76

Characteristic Classes   AM 76   Volume 76 PDF
Author: John Milnor
Publisher: Princeton University Press
ISBN: 140088182X
Size: 30.64 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 340
View: 5442

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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.

Scissors Congruences Group Homology And Characteristic Classes

Scissors Congruences  Group Homology and Characteristic Classes PDF
Author: Johan L. Dupont
Publisher: World Scientific
ISBN: 9810245084
Size: 20.22 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 168
View: 1566

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These lecture notes are based on a series of lectures given at the Nankai Institute of Mathematics in the fall of 1998. They provide an overview of the work of the author and the late Chih-Han Sah on various aspects of Hilbert's Third Problem: Are two Euclidean polyhedra with the same volume ?scissors-congruent?, i.e. can they be subdivided into finitely many pairwise congruent pieces? The book starts from the classical solution of this problem by M Dehn. But generalization to higher dimensions and other geometries quickly leads to a great variety of mathematical topics, such as homology of groups, algebraic K-theory, characteristic classes for flat bundles, and invariants for hyperbolic manifolds. Some of the material, particularly in the chapters on projective configurations, is published here for the first time.