Katsuhiko Kuribayashi
Published 2021-08-30Version 1
By using local systems over simplicial sets with values in differential graded algebras, we consider a framework of rational and ${\mathbb R}$-local homotopy theory for diffeological spaces with arbitrary fundamental groups. Moreover, a spectral sequence converging to the singular de Rham cohomology of an adjunction space is constructed with the pullback of local systems. In case of a stratifold obtained by attaching manifolds, the spectral sequence converges to the original de Rham cohomology, which is due to Souriau, of the stratifold.
The splitting of the de Rham cohomology of soft function algebras is multiplicative
The de Rham cohomology of soft function algebras
The inverse limit topology and profinite descent on Picard groups in $K(n)$-local homotopy theory
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