Abstract:
We generalize Cartan’s logarithmic derivative of a smooth map from a manifold into a Lie group G to smooth maps into a homogeneous space M = G/H, and determine the global monodromy obstruction to reconstructing such maps from infinitesimal data. The logarithmic derivative of the embedding of a submanifold Σ ⊂ M becomes an invariant of Σ under symmetries of the “Klein geometry” M whose analysis is taken up in [SIGMA 14 (2018), 062, 36 pages, arXiv:1703.03851].