A. Gordillo, J. Navarro
Published 2015-03-14Version 1
We describe the ringed-space structure of moduli spaces of jets of linear connections (at a point) as orbit spaces of certain linear representations of the general linear group. Then, we use this fact to prove that the only (scalar) differential invariants associated to linear connections are constant functions, as well as to recover various expressions appearing in the literature regarding the Poincar\'{e} series of these moduli spaces.
Moduli spaces of flat Riemannian metrics on 3- and 4-dimensional closed manifolds
Moduli Spaces of (co)closed $\mathrm{G}_2$-structures on nilmanifolds
Moduli spaces for finite-order jets of Riemannian metrics
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