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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-713de340-8b2c-4503-8251-41eb8d597ab4

Czasopismo

Demonstratio Mathematica

Tytuł artykułu

Grassmann sheaves and the classification of vector sheaves

Autorzy Papatriantafillou, M. H.  Vassiliou, E. 
Treść / Zawartość http://www.degruyter.com/view/j/dema
Warianty tytułu
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  
Wydawca De Gruyter
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, mpapatr@math.uoa.gr
autor Vassiliou, E.
  • Department of Mathematics, University of Athens, Panepistimiopolis, Athens 157 84, Greece, evassil@math.uoa.gr
Bibliografia
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[10] A. Mallios, Modern Differential Geometry in Gauge Theories. Vol. I: Maxwell fields, Vol. II. Yang-Mills fields, Birkhaüser, Boston, 2006/2010.
[11] A. Mallios, P. Ntumba, On a sheaf-theoretic version of the Witt’s decomposition theorem. A Lagrangian perspective , Rend. Circ. Mat. Palermo 58(2) (2009), 155–168.
[12] A. Mallios, P. Ntumba, Fundamentals for symplectic A-modules. Affine Darboux theorem, Rend. Circ. Mat. Palermo 58(2) (2009), 169–198.
[13] A. Mallios, I. Raptis, Finitary spacetime sheaves of quantum causal sets: curving quantum causality, Internat. J. Theoret. Phys. 40 (2001), 1885–1928.
[14] A. Mallios, I. Raptis, Finitary, causal, and quantal vacuum Einstein gravity, Internat. J. Theoret. Phys. 42 (2003), 1479–1619.
[15] A. Mallios, E. Rosinger, Space-time foam dense singularities and de Rham cohomology, Acta Appl. Math. 67 (2001), 59–89.
[16] B. R. Tennison, Sheaf Theory, London Mathematical Society Lecture Note Series 20, Cambridge University Press, Cambridge, 1975.
[17] E. Vassiliou, On the cohomology and geometry of principal sheaves, Demonstration Math. 36 (2003), 289–306.
[18] E. Vassiliou, Geometry of Principal Sheaves, Springer, New York, 2005.
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