Previous |  Up |  Next


fiber product preserving bundle functor; Weil algebra; $r$-jet
We describe the fiber product preserving bundle functors on the category of all morphisms of fibered manifolds in terms of infinite sequences of Weil algebras and actions of the skeleton of the category of $r$-jets by algebra homomorphisms. We deduce an explicit formula for the iteration of two such functors. We characterize the functors with values in vector bundles.
[1] Cabras A., Kolář I.: Flow prolongation of some tangent valued forms. to appear in Acta Mathematica Sinica. MR 2411105
[2] Doupovec M., Kolář I.: Iteration of fiber product preserving bundle functors. Monatsh. Math. 134 (2001), 39–50. MR 1872045 | Zbl 0999.58001
[3] Kolář I.: Functorial prolongations of Lie algebroids. Proceedings Conf. Prague 2004, Charles University, Prague, 2005, 301–309. MR 2268942
[4] Kolář I.: Functorial prolongations of Lie groupoids. to appear in Banach Center Publications. MR 2342859 | Zbl 1115.58003
[5] Kolář I., Cabras A.: On the functorial prolongations of principal bundles. to appear in CMUC. MR 2337425 | Zbl 1150.58002
[6] Kolář I., Michor P. W., Slovák J.: Natural Operations in Differential Geometry. Springer-Verlag, 1993. MR 1202431
[7] Kolář I., Mikulski W. M.: On the fiber product preserving bundle functors. Differential Geometry and Its Applications 11 (1999), 105–115. MR 1712139 | Zbl 0935.58001
[8] Mikulski W. M.: There exists a prolongation functor of infinite order. Časopis pěst. mat. 114 (1989), 57–59. MR 0990118 | Zbl 0672.58002
[9] Mikulski W. M.: Natural transformations of Weil functors into bundle functors. Rend. Circ. Mat. Palermo (2), Suppl. 22 (1989), 177–191. MR 1061799
[10] Weil A.: Théorie des points proches sur les variétes différentielles. Colloque de topol. et géom. diff., Strasbourg (1953), 111–117. MR 0061455
Partner of
EuDML logo