Regularity and Tresse’s theorem for geometric structures. (English. Russian original) Zbl 1148.53011

Sarkisyan, R. A.; Shandra, I. G.

Izv. Math. 72, No. 2, 345-382 (2008); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 2, 151-192 (2008).

Tresse’s theorem about the finitely based invariants of a Lie pseudo-group for the \(k\)-jet space \(J^k\) is established and the regularity of fiber points (local constancy of orbit dimensions) is proved. The paper is a continuation of [R. A. Sarkisyan, Izv. Math. 70, No. 2, 307–362 (2006); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 70, No. 2, 99–158 (2006; Zbl 1106.53010)]. See also A. Tresse [Acta Math. 1–88, see also (1893) Thése présenté à la Faculté des Sciences de Paris, No. 794 (1894; JFM 25.0641.01)]; A. S. Shmelev [Funct. Anal. Appl. 31, No. 2, 119–125 (1997); translation from Funkts. Anal. Prilozh. 31, No. 2, 58–66 (1997; Zbl 0920.58003)].

Reviewer: Maido Rahula (Tartu)

MSC:

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

Keywords:

Lie pseudo-group for jet space; invariants and orbits