2021/08/30 by Katsuhiko Kuribayashi, Kuribayashi, Katsuhiko · 1 citation
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2108.13084
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.