Warianty tytułu
Języki publikacji
Abstrakty
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.
Czasopismo
Rocznik
Tom
Strony
263--270
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
- Department of Mathematics, University of Athens, Panepistimiopolis, Athens 157 84, Greece, mpapatr@math.uoa.gr
autor
- Department of Mathematics, University of Athens, Panepistimiopolis, Athens 157 84, Greece, evassil@math.uoa.gr
Bibliografia
- [1] G. L. Bredon, Sheaf Theory, 2nd Edition, GTM 170, Springer-Verlag, New York, 1997.
- [2] C. H. Dowker, Lectures on Sheaf Theory, Tata Inst. Fund. Research, Bombay, 1962.
- [3] J. Dugundji, Topology, Allyn and Bacon, Boston, 1966.
- [4] R. Godement, Topologie Algébrique et Théorie des Faisceaux, 3ème Édition, Hermann, Paris, 1973.
- [5] D. Husemoller, Fibre Bundles, 3rd Edition, Springer, New York, 1994.
- [6] D. W. Kahn, Introduction to Global Analysis, Academic Press, New York, 1980.
- [7] M. Karoubi, K-Theory. An Introduction, Springer-Verlag, Berlin, 1978.
- [8] S. Lang, Fundamentals of Differential Geometry, GTM 191, Springer, New York, 1999.
- [9] A. Mallios, Geometry of Vector Sheaves. An axiomatic approach to differential geometry, Vols. I–II, Kluwer, Dordrecht, 1998.
- [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-713de340-8b2c-4503-8251-41eb8d597ab4