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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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Maps and vector bundles

Maps and vector bundles

Chapter:
(p.48) 5 Maps and vector bundles
Source:
Differential Geometry
Author(s):

Clifford Henry Taubes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199605880.003.0005

This discussion of maps and vector bundles covers the pull-back construction; pull-backs and Grassmannians; pull-back of differential forms and push-forward of vector fields; invariant forms and vector fields on Lie groups; the exponential map on a matrix group; the exponential map and right/left invariance on Gl(n; ℂ) and its subgroups; and immersion, submersion, and transversality.

Keywords:   pull-back construction, Grassmannians, vector fields, Lie groups, matrix group, exponential map

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