Jet manifolds and natural bundles. (English) Zbl 1236.58006

Saunders, D. J.

Krupka, Demeter (ed.) et al., Handbook of global analysis. Amsterdam: Elsevier (ISBN 978-0-444-52833-9/hbk). 1035-1068 (2008).

Summary: The two concepts forming the subject of this short article were both originally formulated in the nineteen fifties, at a time when the importance of fibre bundles was becoming clear. The idea of a jet appeared in the work of Charles Ehresmann; this is an object which encapsulates the values taken at a point by a map and its derivatives up to some given order. Jets are useful as tools to provide coordinate-free ways of describing constructions such as differential equations, and are particularly convenient where a space of maps, which would normally be infinite-dimensional, can be replaced by a finite-dimensional space of jets. In Section 2 we give the basic definitions and describe various manifolds of jets, paying particular attention to the geometrical structures which are associated with these manifolds.
For the entire collection see [Zbl 1235.58001].

MSC:

58A20	Jets in global analysis
58A32	Natural bundles