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Differential GeometryBundles, Connections, Metrics and Curvature$
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Clifford Henry Taubes

Print publication date: 2011

Print ISBN-13: 9780199605880

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199605880.001.0001

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Curvature polynomials and characteristic classes

Curvature polynomials and characteristic classes

(p.170) 14 Curvature polynomials and characteristic classes
Differential Geometry

Clifford Henry Taubes

Oxford University Press

This chapter explains how the curvatures of connections can be used to construct De Rham cohomology classes that distinguish isomorphism classes of vector bundles and principal bundles. These classes are known as characteristic classes. The discussions cover the Bianchi Identity; characteristic forms; characteristic classes for complex vector bundles and the Chern classes; characteristic classes for real vector bundles and the Pontryagin classes; examples of bundles with nonzero Chern classes; The degree of the map g → gm from SU(2) to itself; and a Chern-Simons form.

Keywords:   curvatures, connections, De Rham cohomology classes, Bianchi Identity, vector bundles, Chern classes, Pontryagin classes

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