Smooth homotopy of diffeological spaces: theory and applications to infinite-dimensional \(C^\infty \)-manifolds. (English) Zbl 1531.58007
Magnot, Jean-Pierre (ed.), Recent advances in diffeologies and their applications. AMS-EMS-SMF special session, Université de Grenoble-Alpes, Grenoble, France, July 18–20, 2022. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 794, 239-258 (2024).
Summary: We present the basic notions and results of our smooth homotopy theory of diffeological spaces and its applications to infinite-dimensional \(C^\infty\)-manifolds, focusing on the fundamental ideas. In particular, smoothing problems for maps, sections, principal bundles, and gauge transformations are discussed.
For the entire collection see [Zbl 1531.53005].
For the entire collection see [Zbl 1531.53005].
MSC:
| 58A40 | Differential spaces |
| 58B10 | Differentiability questions for infinite-dimensional manifolds |
| 18F15 | Abstract manifolds and fiber bundles (category-theoretic aspects) |
| 18N40 | Homotopical algebra, Quillen model categories, derivators |
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