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On differential invariants of geometric structures. (English. Russian original) Zbl 1106.53010
Izv. Math. 70, No. 2, 307-362 (2006); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 70, No. 2, 99-158 (2006).
The main result of this paper (presented in the Shafarevich seminar) is as follows: If \(P\rightarrow X\) is a bundle of geometric objects such that the dimension of its generic fibre exceeds that of its base \(X\), then the number \(t(k)\) of functionally independent differential invariants of degree \(k\) at any sufficiently general point tends to infinity as \(k\) grows.
Also, an asymptotic lower bound for \(t(k)\) is obtained and a generalization of the previous theorem is given.
Reviewer: Radu Miron (Iaşi)

MSC:
53A55 Differential invariants (local theory), geometric objects
58A20 Jets in global analysis
58H05 Pseudogroups and differentiable groupoids
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