Equivariant jets (Q799992)

In the study of equivariant maps, the standard jet terminology is not appropriate: one needs jets along an orbit rather than at a point. Jet bundles (analogous to the usual one) can be defined over orbit type strata of the quotient space V/G: to fit these together is not easy, and the method developed here (using charts) involves choices. Tangent spaces to orbits of jets under right equivalence etc. are next examined. Each of the usual groups has two equivariant analogues: the second is constructed in an appendix. Another new feature is a careful analysis of the use of slices to reduce to a linearized situation. The main new result obtained is that, for each of these groups \(B^ G\) of equivalences, the corresponding set of unstable jets is a (closed) algebraic set in the equivariant jet space; with a companion result for multijets.