Author : Daniel Lehmann
Publisher :
Page : 20 pages
File Size : 35,5 MB
Release : 1999
Category :
ISBN :
A/ Chern Weil Theory for Milnor Classes
Daniel Lehmann
[PDF] A Chern Weil Theory For Milnor Classes eBook
A Chern Weil Theory For Milnor Classes Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of A Chern Weil Theory For Milnor Classes book. This book definitely worth reading, it is an incredibly well-written.
Characteristic Classes
John Willard Milnor
Author : John Willard Milnor
Publisher : Princeton University Press
Page : 342 pages
File Size : 18,26 MB
Release : 1974
Category : Mathematics
ISBN : 9780691081229
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.
A Topological Chern-Weil Theory
Anthony Valiant Phillips
Author : Anthony Valiant Phillips
Publisher : American Mathematical Soc.
Page : 90 pages
File Size : 25,44 MB
Release : 1993
Category : Mathematics
ISBN : 0821825666
We examine the general problem of computing characteristic invariants of principal bundles whose structural group [italic capital]G is a topological group. Under the hypothesis that [italic capital]G has real cohomology finitely generated as an [bold]R-module, we are able to give a completely topological, local method for computing representative cocycles for real characteristic classes; our method applies, for example, to the (homologically) 10-dimensional non-Lie group of Hilton-Roitberg-Stasheff.
Lectures on Chern-Weil Theory and Witten Deformations
Weiping Zhang
Author : Weiping Zhang
Publisher : World Scientific
Page : 131 pages
File Size : 35,2 MB
Release : 2001
Category : Mathematics
ISBN : 9812386580
This invaluable book is based on the notes of a graduate course on differential geometry which the author gave at the Nankai Institute of Mathematics. It consists of two parts: the first part contains an introduction to the geometric theory of characteristic classes due to ShiingOCoshen Chern and Andr(r) Weil, as well as a proof of the GaussOCoBonnetOCoChern theorem based on the MathaiOCoQuillen construction of Thom forms; the second part presents analytic proofs of the Poincar(r)OCoHopf index formula, as well as the Morse inequalities based on deformations introduced by Edward Witten. Contents: ChernOCoWeil Theory for Characteristic Classes; Bott and DuistermaatOCoHeckman Formulas; GaussOCoBonnetOCoChern Theorem; Poincar(r)OCoHopf Index Formula: An Analytic Proof; Morse Inequalities: An Analytic Proof; ThomOCoSmale and Witten Complexes; Atiyah Theorem on Kervaire Semi-characteristic. Readership: Graduate students and researchers in differential geometry, topology and mathematical physics."
Geometry of Characteristic Classes
Shigeyuki Morita
Author : Shigeyuki Morita
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 42,65 MB
Release : 2001
Category : Mathematics
ISBN : 0821821393
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.
Lectures on Chern-Weil Theory and Witten Deformations
Weiping Zhang
Author : Weiping Zhang
Publisher : World Scientific
Page : 131 pages
File Size : 14,22 MB
Release : 2001
Category : Mathematics
ISBN : 9810246854
Drawn from the acclaimed New Princeton Encyclopedia of Poetry and Poetics, the articles in this concise new reference book provide a complete survey of the poetic history and practice in every major national literature or cultural tradition in the world. As with the parent volume, which has sold over 10,000 copies since it was first published in 1993, the intended audience is general readers, journalists, students, teachers, and researchers. The editor's principle of selection was balance, and his goal was to embrace in a structured and reasoned way the diversity of poetry as it is known across the globe today. In compiling material on 106 cultures in 92 national literatures, the book gives full coverage to Indo-European poetries (all the major Celtic, Slavic, Germanic, and Romance languages, as well as other obscure ones such as Hittite), the ancient middle Eastern poetries (Hebrew, Persian, Sumerian, and Assyro-Babylonian), subcontinental Indian poetries (the widest linguistic diversity), Asian and Pacific poetries (Chinese, Japanese, Korean, Vietnamese, Mongolian, and half a dozen others), continental American poetries (all the modern Western cultures and native Indian in North, Central, and South American regions), and African poetries (ancient and emergent, oral and written).
Vector fields on Singular Varieties
Jean-Paul Brasselet
Author : Jean-Paul Brasselet
Publisher : Springer
Page : 242 pages
File Size : 35,48 MB
Release : 2009-11-28
Category : Mathematics
ISBN : 3642052053
Many authors have questioned the use of the index of the vector field, and of the Chern classes, if the underlying space becomes singular. This book discusses their explorations within the framework of the obstruction theory and the Chern-Weil theory.
Topological Chern-Weil Theory
Anthony Valiant Phillips
Author : Anthony Valiant Phillips
Publisher : Oxford University Press, USA
Page : 90 pages
File Size : 34,83 MB
Release : 2014-08-31
Category : MATHEMATICS
ISBN : 9781470400811
This work develops a topological analogue of the classical Chern-Weil theory as a method for computing the characteristic classes of principal bundles whose structural group is not necessarily a Lie group, but only a cohomologically finite topological group. Substitutes for the tools of differential geometry, such as the connection and curvature forms, are taken from algebraic topology, using work of Adams, Brown, Eilenberg-Moore, Milgram, Milnor and Stasheff. The result is a synthesis of the algebraic-topological and differential-geometric approaches to characteristic classes. In contrast to the first approach, specific cocycles are used, so as to highlight the influence of local geometry on global topology. In contrast to the second, calculations are carried out at the small scale rather than the infinitesimal; in fact, this work may be viewed as a systematic extension of the observation that curvature is the infinitesimal form of the defect in parallel translation around a rectangle. This book could be used as a text for an advanced graduate course in algebraic topology.
Geometry of Differential Forms
Shigeyuki Morita
Author : Shigeyuki Morita
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 27,7 MB
Release : 2001
Category : Mathematics
ISBN : 9780821810453
Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated is a detailed description of the Chern-Weil theory. The book can serve as a textbook for undergraduate students and for graduate students in geometry.
Handbook of K-Theory
Eric Friedlander
Author : Eric Friedlander
Publisher : Springer Science & Business Media
Page : 1148 pages
File Size : 25,53 MB
Release : 2005-07-18
Category : Mathematics
ISBN : 354023019X
This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.