Abstract
For complex parallelisable manifolds Γ\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.
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H. Kasuya is supported by JSPS KAKENHI Grant Number JP19H01787.
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KASUYA, H., STELZIG, J. FRÖLICHER SPECTRAL SEQUENCE AND HODGE STRUCTURES ON THE COHOMOLOGY OF COMPLEX PARALLELISABLE MANIFOLDS. Transformation Groups 28, 1595–1606 (2023). https://doi.org/10.1007/s00031-022-09785-x
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DOI: https://doi.org/10.1007/s00031-022-09785-x