Albeverio, Kondratiev, and Röckner have introduced a type of differential geometry, which we call lifted geometry, for the configuration space ${\Gamma }_X$ of any manifold $X$. The name comes from the fact that various elements of the geometry of ${\Gamma }_X$ are constructed via lifting of the corresponding elements of the geometry of $X$. In this note, we construct a general algebraic framework for lifted geometry which can be applied to various “infinite dimensional spaces” associated to $X$. In order to define a lifted...

We give an alternative proof of the stable manifold theorem as an application of the (right and left) inverse mapping theorem on a space of sequences. We investigate the diffeomorphism class of the global stable manifold, a problem which in the general Banach setting gives rise to subtle questions about the possibility of extending germs of diffeomorphisms.