Nosaka, Takefumi De Rham theory and cocycles of cubical sets from smooth quandles. (English) Zbl 1432.55028 Kodai Math. J. 42, No. 1, 111-129 (2019). Given a quandle \(X\) (a quandle is a space with a binary operation that satisfies certain laws akin to those obeyed by conjugation on a group) it is possible to form a classifying space \(BX\) as a cubical set. This paper considers the case where the quandle \(X\) has a manifold structure. The author shows a de Rham theorem for \(BX\) and determines the rational cohomology of \(BX\). The author further examines the contrast between the cohomology groups of \(BX\) and \(BX^{\delta}\) where \(X^{\delta}\) denotes the discrete topology on \(X\). Reviewer: Jonathan Hodgson (Swarthmore) MSC: 55R40 Homology of classifying spaces and characteristic classes in algebraic topology 57R19 Algebraic topology on manifolds and differential topology 55U10 Simplicial sets and complexes in algebraic topology 58J28 Eta-invariants, Chern-Simons invariants Keywords:cubical sets; quandle; de Rham theory; secondary characteristic classes; invariant theory PDFBibTeX XMLCite \textit{T. Nosaka}, Kodai Math. J. 42, No. 1, 111--129 (2019; Zbl 1432.55028) Full Text: DOI arXiv Euclid