Grassmann sheaves and the classification of vector sheaves

• Autorzy: Papatriantafillou, M. H. , Vassiliou, E.
• Języki publikacji: EN

Abstrakty

EN

We classify vector sheaves (an abstraction of vector bundles) by means of a universal Grassmann sheaf. This is done in three steps. Given a sheaf of unital commutative and associative algebras A, we first construct the k-th Grassmann sheaf GA(k, n) of An, whose sections induce vector subsheaves of An of rank k. Next we show that every vector sheaf (a locally free A-module) over a paracompact space is a subsheaf of A∞. In the last step, the foregoing considerations lead to the construction of a universal Grassmann sheaf GA(n), whose global sections classify vector sheaves of rank n over a paracompact space. Note that a homotopy classification is not applicable in this context.

Słowa kluczowe

PL

snopy wektora; snopy Grassmanna; klasyfikacja snopów wektora

EN

vector sheaves; Grassmann sheaves; classification of vector sheaves

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 2
• Strony: 263--270
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Papatriantafillou, M. H.

• Department of Mathematics, University of Athens, Panepistimiopolis, Athens 157 84, Greece,

autor

Vassiliou, E.

• Department of Mathematics, University of Athens, Panepistimiopolis, Athens 157 84, Greece,

Bibliografia

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