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Differential GeometryBundles, Connections, Metrics and Curvature$
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Differential Geometry: Bundles, Connections, Metrics and Curvature

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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Flat connections and holonomy

Flat connections and holonomy

Chapter:
(p.152) 13 Flat connections and holonomy
Source:
Differential Geometry
Author(s):

Clifford Henry Taubes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199605880.003.0013

This chapter examines flat connections. A connection on a principal bundle is said to be flat when its curvature 2-form is identically zero. The discussions cover flat connections on bundles over the circle; foliations; automorphisms of a principal bundle; the fundamental group of a manifold; the flat connections on bundles over M; the universal covering space; holonomy and curvature; and proof of the classification theorem for flat connections.

Keywords:   principal bundle, foliations, automorphisms, manifold, curvature

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