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Demonstratio Mathematica

Tytuł artykułu

Grassmann sheaves and the classification of vector sheaves

Autorzy Papatriantafillou, M. H.  Vassiliou, E. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
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  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2013
Tom Vol. 46, nr 2
Strony 263--270
Opis fizyczny Bibliogr. 18 poz.
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,
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