Synthetic differential geometry of jet bundles (Q1812205)

The author claims that orthodox differential geometry (in particular, the theory of infinite jet bundles within such an orthodox theory) is not suitable for the description of a geometric theory of nonlinear partial differential equations. Following the author, synthetic differential geometry, introduced by Lawvere, is the most suitable framework for the theory of infinite jet bundles. With this promise, the author constructs a theory in which the notion of (nonlinear) connection plays a predominant role. The theory developed is completely intrinsic. Within such a theory contact vector fields of finite type are completely determined. Corrigenda have been published in ibid. 9, No. 3, 473 (2002).