On the homotopy of certain mapping spaces
The author provides a method to compute the homotopy groups of certain subspaces of the space of based self-maps of the total space X in a principal G-bundle over the n-sphere. The method involves identifying the space obtained by collapsing a fibre in X to the base point with the one point union (wedge sum) of the n-sphere and the n-fold suspension of G, and the homotopy sequences for certain fibrations of mapping spaces. The main application is to the space of bundle maps of X into itself.
homotopy groups of subspaces of the space of based self-maps of the total space in a principal bundle over the n-sphere
homotopy sequences for fibrations of mapping spaces
scientific article; zbMATH DE number 4092342
scientific article