There exists a prolongation functor of infinite order. (English) Zbl 0672.58002

Mikulski, W. M.

Čas. Pěstování Mat. 114, No. 1, 57-59 (1989).

A classical result by R. S. Palais and C. L. Terng reads that every prolongation functor on the category \(Mf_ n\) of n-dimensional manifolds and their local diffeomorphisms has finite order [Topology 16, 271-277 (1977; Zbl 0359.58004)]. The author constructs a prolongation functor on the category of all manifolds and all smooth maps with the property that the sequence of the orders of its restrictions to \(Mf_ n\) tends to infinity.

Reviewer: I.Kolář

MSC:

58A20	Jets in global analysis
53A55	Differential invariants (local theory), geometric objects

Keywords:

natural bundle; geometric functor on the category of smooth; manifolds

Citations:

Zbl 0359.58004