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THEODORE VORONOV DIFFERENTIAL GEOMETRY. Spring 2007 under construction Connection on a vector bundle Basic notions related with vector bundles De nition. Recollection Examples T M tautological bundle over projective spaces. Sections. Module structure. Let E B be a vector bundle of rank k. From now on we use the notation Ex p 1 x for the ber over x B. It is a vector space. Let B E denote the space of sections of E* Sections are always assumed to be smooth. It is a vector space in nite...

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