2024
DOI: 10.1090/conm/794/15939
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Smooth homotopy of diffeological spaces: theory and applications to infinite-dimensional 𝐢^{∞}-manifolds

Hiroshi Kihara

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.

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