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arXiv · 2011.07905

Fr\"olicher spectral sequence and Hodge structures on the cohomology of complex parallelisable manifolds

Hisashi Kasuya·Jonas Stelzig
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Abstract

For complex parallelisable manifolds $\Gamma\backslash G$, with $G$ a solvable or semisimple complex Lie group, the Fr\"olicher 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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Hisashi Kasuya, Jonas Stelzig. 2020-11-16. Fr\"olicher spectral sequence and Hodge structures on the cohomology of complex parallelisable manifolds. https://arxiv.org/abs/2011.07905

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