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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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Algebra of vector bundles

Algebra of vector bundles

(p.39) 4 Algebra of vector bundles
Differential Geometry

Clifford Henry Taubes

Oxford University Press

Any linear operation that can be performed to generate a new vector space from a given set of initial vector spaces can be done fibre-wise with an analogous set of vector bundles to generate a new vector bundle. This chapter describes the most important examples. The discussions cover subbundles; quotient bundles; the dual bundle; bundles of homomorphisms; tensor product bundles; the direct sum; and tensor powers.

Keywords:   vector spaces, subbundles, quotient bundles, dual bundle, homomorphisms, tensor product bundles, tensor powers

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