Dolbeault cohomology of nilmanifolds with left-invariant complex structure
S\"onke Rollenske
TL;DR
This paper examines the conjecture that Dolbeault cohomology of nilmanifolds with left-invariant complex structures can be computed via Lie-algebra cohomology, discussing evidence and applications.
Contribution
It reviews existing evidence supporting the conjecture and explores its implications and applications in complex geometry.
Findings
Evidence supports the conjecture in specific cases.
Potential applications in complex geometry and topology.
Open problems and future directions discussed.
Abstract
We discuss the known evidence for the conjecture that the Dolbeault cohomology of nilmanifolds with left-invariant complex structure can be computed as Lie-algebra cohomology and also mention some applications.
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Taxonomy
TopicsGeometry and complex manifolds · Advanced Algebra and Geometry · Advanced Topics in Algebra