Journal of Lie Theory 27 (2017), No. 4, 915--941
Copyright Heldermann Verlag 2017
Primary Spectrum of C∞(M) and Jet Theory
Ricardo J. Alonso-Blanco
Department of Mathematics, University of Salamanca, Plaza de la Merced 1-4, 37004 Salamanca, Spain
ricardo@usal.es
Jesús Muñoz-Díaz
Department of Mathematics, University of Salamanca, Plaza de la Merced 1-4, 37004 Salamanca, Spain
clint@usal.es
We consider, for each smooth manifold M, the set M of all primary ideals of C∞(M) which are closed and whose radical is maximal. The classical Lie theory of jets (jets of submanifolds) must be extended to M in order to have nice functorial properties. We will begin with the purely algebraic notions, referred always to the ring C∞(M). Subsequently, the differentiable structures on each jet space of a given type will be introduced. The theory of contact systems, which generalizes the classical one, has a purely algebraic part and another one which depends on the differentiable structures.
Keywords: Jets, primary ideals, rings of functions, spectrum, contact system.
MSC: 58A20
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