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

DOI10.1090/conm/794/15939MaRDI QIDQ6120752

Hiroshi Kihara

Publication date: 21 February 2024

Published in: Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

model categoryconvenient calculussmooth homotopysmoothing theorem

Mathematics Subject Classification ID

Differentiability questions for infinite-dimensional manifolds (58B10) Differential spaces (58A40) Homotopical algebra, Quillen model categories, derivators (18N40) Abstract manifolds and fiber bundles (category-theoretic aspects) (18F15)

Cites Work

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• The \(D\)-topology for diffeological spaces
• Smooth classifying spaces
• Smooth constructions of homotopy-coherent actions
• The homotopy theory of diffeological spaces
• Lie group structures on symmetry groups of principal bundles
• Homotopy theory of infinite dimensional manifolds
• Partitions of unity in the theory of fibrations
• Model category of diffeological spaces
• On Spaces Having the Homotopy Type of a CW-Complex
• A model category structure on the category of simplicial categories
• Equivalences of smooth and continuous principal bundles with infinite-dimensional structure group
• Manifolds Modelled on R ∞ or Bounded Weak- ∗ Topologies
• Simplicial homotopy theory
• Smooth Homotopy of Infinite-Dimensional 𝐶^{∞}-Manifolds