A rank theorem for analytic maps between power series spaces
The main result is a rank theorem for analytic mappings (induced by substitution) between spaces of convergent power series. This is used to show that certain isotropy groups are Lie subgroups of infinite- dimensional Lie groups. A spectacular consequence of this result is that reduced hypersurface germs of dimension \(\geq 2\) are determined up to isomorphism by their Lie group of embedded automorphisms.
scientific article; zbMATH DE number 753834
scientific article