%0 Journal Article
%T Closedness of the tangent spaces to the orbits of proper actions
%A Madeleine Jotz
%A Karl-Hermann Neeb
%J Mathematics
%D 2008
%I arXiv
%X In this note we show that for any proper action of a Banach--Lie group $G$ on a Banach manifold $M$, the corresponding tangent maps $\g \to T_x(M)$ have closed range for each $x \in M$, i.e., the tangent spaces of the orbits are closed. As a consequence, for each free proper action on a Hilbert manifold, the quotient $M/G$ carries a natural manifold structure.
%U http://arxiv.org/abs/0804.4858v1