Grassmann sheaves and the classification of vector sheaves

Details Grassmann sheaves and the classification of vector sheaves Grassmann sheaves and the classification of vector sheaves

2009-05-06

arxiv.org/abs/0905.0807v1

Mathematics

Category Theory

Latex, 8 pages

Scientific paper

Given a sheaf of unital commutative and associative algebras A, first we construct the k-th Grassmann sheaf G_A(k,n) of A^n whose sections induce vector subsheaves of A^n of rank k. Next we show that every vector sheaf over a paracompact space is a subsheaf of A^{\infty}. Finally, applying the preceding results to the universal Grassmann sheaf G_A(n), we prove that vector sheaves of rank n over a paracompact space are classified by the global sections of G_A(n).

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