Characteristic Classes

Characteristic Classes PDF
Author: John Willard Milnor
Publisher: Princeton University Press
Category : Mathematics
Languages : en
Pages : 330
View: 6084

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Book Description:
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.


From Calculus To Cohomology

From Calculus to Cohomology PDF
Author: Ib H. Madsen
Publisher: Cambridge University Press
Category : Mathematics
Languages : en
Pages : 286
View: 563

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Book Description:
An introductory textbook on cohomology and curvature with emphasis on applications.


Geometry Of Characteristic Classes

Geometry of Characteristic Classes PDF
Author: Shigeyuki Morita
Publisher: American Mathematical Soc.
Category : Mathematics
Languages : en
Pages : 185
View: 201

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


Characteristic Classes

Characteristic Classes PDF
Author: John Willard Milnor
Publisher: Princeton University Press
Category : Mathematics
Languages : en
Pages : 330
View: 2647

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Book Description:
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.


Nilpotent Orbits Primitive Ideals And Characteristic Classes

Nilpotent Orbits  Primitive Ideals  and Characteristic Classes PDF
Author: Walter Borho
Publisher: Springer Science & Business Media
Category : Mathematics
Languages : en
Pages : 134
View: 1255

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Book Description:
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.