2020/02/17 by Katsuhiko Kuribayashi, Kuribayashi, Katsuhiko
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons #Sphingolipid Metabolism and Signaling
paper · pdf · doi:10.48550/arxiv.2002.06802
openalex publication_date 2020/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
There are two de Rham complexes in diffeology. The original one is due to Souriau and the other one is the singular de Rham complex defined by a simplicial differential graded algebra. We compare the first de Rham cohomology groups of the two complexes within the Čech--de Rham spectral sequence by making use of the \it factor map which connects the two de Rham complexes. As a consequence, it follows that the singular de Rham cohomology algebra of the irrational torus Tθ is isomorphic to the tensor product of the original de Rham cohomology and the exterior algebra generated by a non-trivial flow bundle over Tθ.