Topological Chern-Weil Theory

Topological Chern-Weil Theory
Author :
Publisher : Oxford University Press, USA
Total Pages : 90
Release :
ISBN-10 : 1470400812
ISBN-13 : 9781470400811
Rating : 4/5 (811 Downloads)

Book Synopsis Topological Chern-Weil Theory by : Anthony Valiant Phillips

Download or read book Topological Chern-Weil Theory written by Anthony Valiant Phillips and published by Oxford University Press, USA. This book was released on 2014-08-31 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Topological Chern-Weil Theory Related Books

Topological Chern-Weil Theory
Language: en
Pages: 90
Authors: Anthony Valiant Phillips
Categories: MATHEMATICS
Type: BOOK - Published: 2014-08-31 - Publisher: Oxford University Press, USA

DOWNLOAD EBOOK

This work develops a topological analogue of the classical Chern-Weil theory as a method for computing the characteristic classes of principal bundles whose str
A Topological Chern-Weil Theory
Language: en
Pages: 90
Authors: Anthony Valiant Phillips
Categories: Mathematics
Type: BOOK - Published: 1993 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

We examine the general problem of computing characteristic invariants of principal bundles whose structural group [italic capital]G is a topological group. Unde
Lectures On Chern-weil Theory And Witten Deformations
Language: en
Pages: 131
Authors: Weiping Zhang
Categories: Mathematics
Type: BOOK - Published: 2001-09-21 - Publisher: World Scientific

DOWNLOAD EBOOK

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 consis
Characteristic Classes. (AM-76), Volume 76
Language: en
Pages: 339
Authors: John Milnor
Categories: Mathematics
Type: BOOK - Published: 2016-03-02 - Publisher: Princeton University Press

DOWNLOAD EBOOK

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomo
Lecture Notes on Chern-Simons-Witten Theory
Language: en
Pages: 214
Authors: Sen Hu
Categories: Gauge fields (Physics).
Type: BOOK - Published: 2001 - Publisher: World Scientific

DOWNLOAD EBOOK

This monograph is based on lectures on topological quantum field theory given in 1989 at Princeton University by E. Witten, in which he unified several importan