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On the simplicial structure of some Weil bundles. (English) Zbl 0981.58001
Slovák, Jan (ed.) et al., The proceedings of the 19th Winter School “Geometry and physics”, Srní, Czech Republic, January 9-15, 1999. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 63, 131-140 (2000).
The author considers the problem to give explicit descriptions for several types of bundles on smooth manifolds, naturally related with the bundle of \(k\)-dimensional velocities, or \(k\)-jets. In fact, this kind of bundles are very natural objects in differential geometry, mechanics and Lagrangian dynamics. For this the author considers Weil bundles that arose from Weil algebras. If a suitable combinatorial data is provided by a simplicial coloured structure, then the author describes the corresponding Weil bundle and its Weil algebra.
For the entire collection see [Zbl 0940.00040].
58A20 Jets in global analysis