Closedness of the tangent spaces to the orbits of proper actions

Madeleine Jotz; Karl-Hermann Neeb

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arXiv · 0804.4858

Closedness of the tangent spaces to the orbits of proper actions

Madeleine Jotz·Karl-Hermann Neeb

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Abstract

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.

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Madeleine Jotz, Karl-Hermann Neeb. 2008-04-30. Closedness of the tangent spaces to the orbits of proper actions. https://arxiv.org/abs/0804.4858

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