2020/11/16 by Hisashi Kasuya, Kasuya, Hisashi, Jonas Stelzig +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2011.07905
openalex publication_date 2020/11/16 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
For complex parallelisable manifolds Γ\backslash G, with G a solvable or semisimple complex Lie group, the Frölicher spectral sequence degenerates at the second page. In the solvable case, the de-Rham cohomology carries a pure Hodge structure. In contrast, in the semisimple case, purity depends on the lattice, but there is always a direct summand of the de Rham cohomology which does carry a pure Hodge structure and is independent of the lattice.