Smooth homotopy of diffeological spaces: theory and applications to infinite-dimensional 𝐶^{∞}-manifolds

Abstract

We present the basic notions and results of our smooth homotopy theory of diffeological spaces and its applications to infinite-dimensional C ∞ C^\infty -manifolds, focusing on the fundamental ideas. In particular, smoothing problems for maps, sections, principal bundles, and gauge transformations are discussed.