Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 18 (2008), No. 3, 517--521Copyright Heldermann Verlag 2008 Closedness of the Tangent Spaces to the Orbits of Proper Actions Madeleine Jotz Dép. de Mathématiques, Ecole Polytechnique Fédérale, 1015 Lausanne, Switzerland madeleine.jotz@epfl.ch Karl-Hermann Neeb Fachbereich Mathematik, Technische Universität, Schlossgartenstrasse 7, 64289 Darmstadt, Germany neeb@mathematik.tu-darmstadt.de [Abstract-pdf] We show that for any proper action of a Banach-Lie group $G$ on a Banach manifold $M$, the corresponding tangent maps ${\frak g} \to T_x(M)$ 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. Keywords: Banach Lie group, Banach manifold, proper action. MSC: 22E65, 58B25, 57E20 [ Fulltext-pdf  (152  KB)] for subscribers only.