FRÖLICHER SPECTRAL SEQUENCE AND HODGE STRUCTURES ON THE COHOMOLOGY OF COMPLEX PARALLELISABLE MANIFOLDS

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 latti...

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Bibliographic Details
Published in:Transformation groups 2023-12, Vol.28 (4), p.1595-1606
Main Authors: KASUYA, H., STELZIG, J.
Format: Article
Language:English
Subjects:
Algebra
Homology
Lattices (mathematics)
Lie Groups
Manifolds
Mathematics
Mathematics and Statistics
Topological Groups
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Summary: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.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-022-09785-x