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We study the cohomological classification of principal sheaves, the latter being defined in a slightly different way than in [6], a fact allowing to consider on them geometrical objects like connections. The classification of vector sheaves (studied in [10]) is now a corollary of the classification of their principal sheaves of frames. In particular, principal sheaves with an abelian structural sheaf, equipped (the former) with a connection, admit a hypercohomological classification generalizing that of Maxwell fields given in [10].
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Czasopismo
Rocznik
Tom
Strony
289--306
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- University of Athens, Department of Mathematics, Panepistimiopolis, Athens 157 84, Greece
Bibliografia
- [1] N. Bourbaki, Théorie des Ensembles, Hermann, Paris, 1967.
- [2] N. Bourbaki, Algèbre, Chap. 1-3, Hermann, Paris, 1970.
- [3] G. L. Bredon, Sheaf Theory, Springer-Verlag, Berlin, 1997.
- [4] J. L. Brylinski, Loop Spaces, Characteristic Classes and Geometric Quantization, Birkhauser, Boston, 1993
- [5] R. Godement, Topologie Algébrique et Théorie des Faisceaux, Hermann, Paris, 1973.
- [6] A. Grothendieck, A General Theory of Fibre Spaces with Structural Sheaf, Kansas University, 1957.
- [7] M. Heller, Algebraic foundations of the theory of differential spaces, Demonstratio Math. 24 (1991), 349-364.
- [8] M. Heller, P. Multarzyński and W. Sasin, The algebraic approach to space-time geometry, Acta Cosmologica 16 (1989), 53-85.
- [9] F. Hirzebruch, Topological Methods in Algebraic Geometry, Springer-Verlag, Berlin, 1978.
- [10] A. Mallios, Geometry of Vector Sheaves, Vols. I, II, Kluwer Acad. Publ., Dordrecht, 1998.
- [11] A. Mallios, Abstract differential geometry, general relativity, and singularities, Unsolved Problems on Mathematics for the 21st Century, J. M. Abe and S. Tanaka (Eds), IOS Press, 2001.
- [12] A. Mallios and E. Rosinger, Abstract differential geometry, differential algebras of generalized functions, and de Rham cohomology, Acta Appl. Mathem. 55 (1999), 231-250.
- [13] A. Mallios and E. Rosinger, Space-time foam dense singularities and de Rham cohomology, Acta Appl. Mathem. 67 (2001), 59-89.
- [14] M. A. Mostow, The differentiate space structures of Milnor classifying spaces, simplicial complexes and geometric relations, J. Differential Geometry 14 (1979), 255-293.
- [15] I. Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. USA 42 (1956), 359-363.
- [16] R. Sikorski, Differential modules, Colloq. Math. 24 (1971), 45-79.
- [17] J. W. Smith, The de Rham theorem for general spaces, Tôhoku Math. J. 17 (1966), 115-135.
- [18] E. Vassiliou, On Mallios' A-connections as connections on principal sheaves, Note Mat. 14 (1994), 237-249 (1997).
- [19] E. Vassiliou, Transformations of sheaf connections, Balkan J. Geom. Appl. 1 (1996), 117-132.
- [20] E. Vassiliou, Connections on principal sheaves, New Developments in Differential Geometry, Budapest 1996, (J. Szenthe, Editor), Kluwer, 459-473 (1999).
- [21] E. Vassiliou, On the geometry of associated sheaves, Bull. Greek Math. Soc. 44 (2000), 157-170.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-PWA3-0007-0004