1. Local systems in diffeology.
- Author
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Kuribayashi, Katsuhiko
- Subjects
- *
DIFFERENTIAL algebra , *ALGEBRAIC spaces , *HOMOTOPY equivalences , *ALGEBRA , *HOMOTOPY theory - Abstract
By making use of Halperin's local systems over simplicial sets and the model structure of the category of diffeological spaces due to Kihara, we introduce a framework of rational homotopy theory for such smooth spaces with arbitrary fundamental groups. As a consequence, we have an equivalence between the homotopy categories of fibrewise rational diffeological spaces and an algebraic category of minimal local systems elaborated by Gómez-Tato, Halperin and Tanré. In the latter half of this article, a spectral sequence converging to the singular de Rham cohomology of a diffeological adjunction space is constructed with the pullback of relevant local systems. In case of a stratifold obtained by attaching manifolds, the spectral sequence converges to the Souriau–de Rham cohomology algebra of the diffeological space. By using the pullback construction, we also discuss a local system model for a topological homotopy pushout. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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