Warianty tytułu
Języki publikacji
Abstrakty
We present the generalized Stokes theorem for R-linear forms on Lie algebroids (which can be non-local). The Stokes formula on forms is applied to prove that two homotopic homomorphisms of Lie algebroids imply the existence of a chain operator joining their pullback operators.
Czasopismo
Rocznik
Tom
Strony
117-131
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Institute of Mathematics, Technical University of Łódź, Wólczańska 215, 90-924 Łódź Poland, bogdan.balcerzak@p.lodz.pl
Bibliografia
- [1] B. Balcerzak, Modular classes of Lie algebroids homomorphisms as some the Chern-Simons forms, Univ. Iagel. Acta Math. 47 (2009), 11-28.
- [2] R. Bott, Lectures on Characteristic Classes and Foliations, Lecture Notes in Math. 279, Springer, Berlin, 1972.
- [3] M. Crainic, Connections up to homotopy and characteristic classes, preprint (2000), bttp://arxiv.org/abs/math/0010085v2.
- [4] M. Crainic and R. L. Fernandes, Secondary characteristic classes of Lie algebroids, in: Quantum Field Theory and Noncommutative Geometry, Lecture Notes in Phys. 662, Springer, Berlin (2005), 157-176.
- [5] S. Evens, J.-H. Lu and A. Weinstein, Transverse measures, the modular class and a cohomology pairing for Lie algebroids, Q. J. Math. 50 (1999), 417-436.
- [6] J.-C. Herz, Pseudo-algebres de Lie, I, II, C. R. Math. Acad. Sci. Paris 263 (1953), 1935-1937,2289-2291.
- [7] R J. Higgins and K. C. H. Mackenzie, Algebraic constructions in the category of Lie algebroids, J. Algebra 129 (1990), 194-230.
- [8] Y. Kosmann-Schwarzbach, C. Laurent-Gengoux and A. Weinstein, Modular classes of Lie algebroid morphisms. Transform. Groups 13 (2008), 727-755.
- [9] J. Kubarski, The Chern- Weil Homomorphism of Regular Lie Algebroids, Publications du Departement de Mathematiques, Nouvelle Sen A, University Claude Bernard, Lyon, 1991.
- [10] J. Kubarski, Invariant cohomology of regular Lie algebroids, in: Analysis and Geometry in Foliated Manifolds, World Scientific Publishing, Singapore (1995), 137-151.
- [11] K. C. H. Mackenzie, General Theory of Lie Groupoids and Lie Algebroids, London Math. Soc. Lecture Note Ser. 213, Cambridge University Press, 2005.
- [12] J. Pradines, Theorie de Lie pour les groupides diffdrentiables, calcul differentiel dans la categorie des groupides infinitesimaux, C. R. Math. Acad. Sci. Paris 264 (1967), 245-248.
- [13] I. Vaisman, Characteristic classes of Lie algebroid morphisms, Differential Geom. Appl. 28 (2010), 635-647.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD7-0033-0032