That which we call a manifold ...
Dr Andrew Stacey (NTNU Trondheim)
Monday 4th March, 2013 16:00-17:00 Mathematics 203
It is well known that the mapping space of two finite dimensional manifolds can be given the structure of an infinite dimensional manifold modelled on Fréchet spaces (provided the source is compact). However, it is not that the charts on the original manifolds give the charts on the mapping space: it is a little bit more complicated than that. These complications become important when one extends this construction, either to spaces more general than manifolds or to properties other than being locally linear. In this talk, I shall show how to describe the type of property needed to transport local properties of a space to local properties of its mapping space. As an application, we shall show that applying the mapping construction to a regular map is again regular.